Our research is in the field of nonlinear waves, lying听at the nexus of applied mathematics and physics. 听Mathematically, the nonlinear waves that we investigate are solutions to nonlinear, dispersive partial differential equations. 听Physically, this field has been driven by applications ranging from classical (geophysical fluid dynamics) to modern physics (nonlinear optics and quantum/condensed matter) in which wave speed depends upon the countervailing effects of wave amplitude and wavelength.听 In these physical environments, coherent structures such as solitons or solitary waves, periodic waves, and听听play a decisive role in the dynamics of large amplitude excitations.听 The Dispersive Hydrodynamics Lab investigates the mathematics of coherent structures and their dynamics in nonlinear dispersive partial differential equations with particular application to fluid dynamics where we develop in-house experiments to test our mathematical predictions.听 Research also focuses upon nonlinear wave applications听in magnetic media where a variety of coherent spin wave, solitonic, and hydrodynamic-like structures are studied.听 Methods employed include mathematical modeling, analysis, asymptotics, Whitham modulation theory, numerical analysis, and in-house experiment. Whenever possible, comparisons with experiment are carried out.听

The generation of DSWs represents a universal mechanism to resolve hydrodynamic singularities in dispersive media. Physical manifestations of DSWs include undular bores on shallow water and in the atmosphere (the Morning Glory), nonlinear diffraction patterns in optics, and matter waves in ultracold atoms. Any approximately conservative, nonlinear, hydrodynamic medium exhibiting weak dispersion can develop DSWs. The mathematical description of DSWs involves a synthesis of methods from hyperbolic quasi-linear systems, asymptotics, and soliton theory. This research is currently supported by the National Science Foundation through听.听

Ferromagnetic media provide a source of rich nonlinear, dispersive phenomena with practical import. Theoretical and technological developments have stimulated the field of nanomagnetism by the introduction of spin polarized currents as a means to excite magnetization dynamics at the nanometer scale in patterned environments. Strongly nonlinear magnetic solitons were听recently observed听in a nanomagnetic system. This solitary wave or "droplet" joins the domain wall and magnetic vortex as a fundamental and distinct object in nanomagnetism with similar potential for fruitful science. Marrying the Lab's research on fluid dynamics听with the field of magnetic materials, we have also been developing the dispersive hydrodynamic description of magnetic materials.

External Listings:听听, ,听

Manuscripts in Review

  1. Yifeng Mao and Mark A. Hoefer,听Experimental investigations of linear and nonlinear periodic traveling waves in a viscous fluid conduit, .
  2. Mingyu Hu, Ezio Iacocca, and Mark Hoefer,听The spin piston problem for a ferromagnetic thin film, .

鈥�Journal Publications

  1. Samuel J. Ryskamp, Mark A. Hoefer, and Gino Biondini,听Modulation theory for soliton resonance and Mach reflection, Proceedings of the Royal Society A,听accepted.听 ()
  2. Mingyu Hu, Ezio Iacocca, Mark A. Hoefer,听Spin-injection-generated shock waves and solitons in a ferromagnetic thin film鈥�, . ()
  3. Kiera van der Sande, Gennady A. El, and Mark A. Hoefer,听Dynamic soliton鈥搈ean flow interaction with non-convex flux, . (reprint听漏听)
  4. T. Congy, G. A. El, M. A. Hoefer, and M. Shearer,听Dispersive Riemann problem for the Benjamin-Bona-Mahony equation,听. ()
  5. Samuel J. Ryskamp, Mark A. Hoefer, and Gino Biondini,听Oblique interactions between solitons and mean flows in the Kadomtsev-Petviashvili equation, . ()
  6. Adam L. Binswanger, Mark A. Hoefer, Boaz Ilan, and Patrick Sprenger,听Whitham modulation theory for generalized Whitham equations and a general criterion for modulational instability, . ().
  7. Samuel Ryskamp, Michelle D. Maiden, Gino Biondini,听and Mark听A. Hoefer,听Evolution of truncated and bent gravity wave solitons:听the Mach expansion problem, . (reprint听漏听)
  8. Gino Biondini, Mark A. Hoefer, and A. Moro,听Integrability, exact reductions and special solutions of the KP-Whitham equations, . ()
  9. P. Sprenger and M. A. Hoefer,听Discontinuous shock solutions of the Whitham modulation equations as zero dispersion limits of traveling waves, . ()
  10. M. D. Maiden, N. A. Franco, E. G. Webb, G. A. El, and M. A. Hoefer, Solitary wave fission of a large disturbance in a viscous fluid conduit, 听().
  11. Ezio Iacocca and Mark A. Hoefer,听Perspectives on spin hydrodynamics in ferromagnetic materials, .
  12. T. Congy, G. A. El, and M. A. Hoefer,听Interaction of linear modulated waves with unsteady dispersive hydrodynamic states with application to shallow water waves, .听()
  13. Richard O. Moore and Mark A. Hoefer,听Stochastic ejection of nanocontact droplet solitons via drift instability, . (reprint)
  14. Dalton V. Valentine, Michelle D. Maiden, and Mark A. Hoefer,听Controlling Dispersive Hydrodynamic Wavebreaking in a Viscous Fluid Conduit,听. (reprint)
  15. Ezio Iacocca and Mark A. Hoefer,听Hydrodynamic description of long-distance spin transport through noncollinear magnetization states:听 the role of dispersion, nonlinearity, and damping,听. (reprint)
  16. E. Iacocca, T-M. Liu, A. H. Reid, Z. Fu, S. Ruta, P. W. Granitzka, E. Jal, S. Bonetti, A. X. Gray, C. E. Graves, R. Kukreja, Z. Chen, D. J. Higley, T. Chase, L. Le Guyader, K. Hirsch, H. Ohldag, W. F. Schlotter, G. L. Dakovski, G. Coslovich, M. C. Hoffmann, S. Carron, A. Tsukamoto, M. Savoini, A. Kirilyuk, A. V. Kimel, Th. Rasing, J. St枚hr, R. F. L. Evans, T. Ostler, R. W. Chantrell, M. A. Hoefer, T. J. Silva, and H. A. D眉rr,听Spin-current-mediated rapid magnon localization and coalescence after ultrafast optical pumping of ferromagnetic alloys,听. (open access) (news)
  17. Patrick Sprenger, Mark A. Hoefer, and Ezio Iacocca,听Magnonic Band Structure Established by Chiral Spin-Density Waves in Thin Film Ferromagnets,听. ()
  18. T. Congy, G. A. El, M. A. Hoefer, and M. Shearer,听Nonlinear Schr枚dinger equations and the universal description of dispersive shock wave structure,听. ()
  19. Mark A. Hoefer, Noel F. Smyth, and Patrick Sprenger,听Modulation theory solution for nonlinearly resonant, fifth order Korteweg-de Vries non-classical traveling dispersive shock waves, .
  20. M. E. Mossman, M. A. Hoefer, K. Julien, P. Kevrekidis, P. Engels,听Dissipative shock waves generated by a quantum-mechanical piston, . (open access)
  21. M.听D. Maiden, D.听V. Anderson, N.听A. Franco, G.听A. El, and M.听A. Hoefer, Solitonic Dispersive Hydrodynamics: Theory and Observation,听. (reprint)
  22. M. Ruth, E. Iacocca, P. G. Kevrekidis, and M. A. Hoefer, Transverse instabilities of stripe domains in magnetic thin films with perpendicular magnetic anisotropy. . (reprint)
  23. P. Sprenger, M. A. Hoefer, and G. A. El,听Hydrodynamic Optical Soliton Tunneling,听. (reprint)
  24. Denys Dutykh, Mark Hoefer, and Dimitrios Mitsotakis, Solitary wave solutions and their interactions for fully nonlinear water waves with surface tension in the generalized Serre equations, .
  25. E. Iacocca, T. J. Silva, and M. A. Hoefer, Symmetry-broken dissipative exchange flows in thin-film ferromagnets with in-plane anisotropy, . (reprint)
  26. G. El, M. A. Hoefer, and M. Shearer,听Stationary expansion shocks for a regularized Boussinesq system, .听(r) (1 of 4 )
  27. P. A. P. Janantha, P. Sprenger, M. A. Hoefer, and M. Wu,听Observation of self-cavitating envelope dispersive shock waves in Yttrium Iron Garnet thin films, . (reprint) 听
  28. M. A. Hoefer, G. A. El, and A. M. Kamchatnov,听Oblique spatial dispersive shock waves in nonlinear Schr枚dinger flows, (reprint)
  29. E. Iacocca and M. A. Hoefer, Vortex-Antivortex proliferation from an obstacle in thin film ferromagnets, .听(reprint)听
  30. G. A. El, M. A. Hoefer, and M. Shearer,听Dispersive and diffusive-dispersive shock waves for non-convex conservation laws, . 听()
  31. E. Iacocca, T. J. Silva, and M. A. Hoefer,听Breaking of Galilean invariance in the hydrodynamic formulation of ferromagnetic thin films, . (reprint, news)
  32. P. Sprenger and M. A. Hoefer,听Shock waves in dispersive hydrodynamics with non-convex dispersion, .听(reprint, news)
  33. M. D. Maiden and M. A. Hoefer,听Modulations of viscous fluid conduit periodic waves, .听(reprint, news)
  34. M. A. Hoefer and B. Ilan,听Onset of transverse instabilities of confined dark solitons,听.听(reprint)
  35. M. D. Maiden, N. K. Lowman, D. V. Anderson, M. E. Schubert, and M. A. Hoefer,听Observation of dispersive shock waves, solitons, and their interactions in viscous fluid conduits,听. (reprint,听movies,听news)
  36. S. Chung, A. Eklund, E. Iacocca, S. M. Mohseni, S. R. Sani, L. Bookman, M. A. Hoefer, R. K. Dumas, and J.听脜kerman,听Magnetic droplet nucleation boundary in orthogonal spin-torque nano-oscillators,听听(open access) (news)
  37. G. Biondini, G. A. El, M. A. Hoefer, and P. D. Miller,听Dispersive Hydrodynamics: 听Preface, . 听Special Issue on .
  38. G. A. El and M. A. Hoefer,听Dispersive shock waves and modulation theory,听. 听Review article in Special Issue on听. ().
  39. G. A. El, M. A. Hoefer, and M. Shearer,听Expansion shock waves in regularized shallow-water theory,听.听()
  40. P. Wills, E. Iacocca, and M. A. Hoefer,听Deterministic drift instability and stochastic thermal perturbations of magnetic dissipative droplet solitons,听. (reprint)
  41. L. D. Bookman and M. A. Hoefer,听Perturbation theory for propagating magnetic droplet solitons,听. (author postprint)
  42. N. K. Lowman, M. A. Hoefer, and G. A. El,听Interactions of large amplitude solitary waves in viscous fluid conduits,听. (reprint听漏听)
  43. M. D. Maiden, L. D. Bookman, and M. A. Hoefer,听Attraction, merger, reflection, and annihilation in magnetic droplet soliton scattering,听. (reprint)
  44. S. Chung, S. M. Mohseni, S. R. Sani, E. Iacocca, R. K. Dumas, T. N. Anh Nguyen, Ye. Pogoryelov, P. K. Muduli, A. Eklund, M. A. Hoefer, and J. 脜kerman,听Spin transfer torque generated magnetic droplet solitons (invited),听. (reprint)
  45. M. A. Hoefer,听Shock waves in dispersive Eulerian fluids,听. (reprint)
  46. E. Iacocca, R. K. Dumas, L. D. Bookman, M. S. Mohseni, S. Chung, M. A. Hoefer, and J. 脜kerman,听Confined dissipative droplet solitons in spin-valve nanowires with perpendicular magnetic anisotropy,听. (reprint)
  47. L. D. Bookman, and M. A. Hoefer,听Analytical theory of modulated magnetic solitons,听. (reprint)
  48. N. K. Lowman and M. A. Hoefer,听Dispersive hydrodynamics in viscous fluid conduits,听. (reprint)
  49. N. K. Lowman and M. A. Hoefer,听Fermionic shock waves: 听distinguishing dissipative versus dispersive regularizations,听. (reprint)
  50. S. M. Mohseni, S. R. Sani, J. Persson,听 T. N. Anh Nguyen, S. Chung, Ye. Pogoryelov, P. K. Muduli, E.听 Iacocca, A. Eklund, R. K. Dumas, S.听 Bonetti, A. Deac, M. A. Hoefer, and J. 脜kerman,听Spin Torque鈥揋enerated Magnetic Droplet Solitons,听. (reprint)
  51. N. K. Lowman and M. A. Hoefer,听Dispersive shock waves in viscously deformable media,听. (reprint听漏听)
  52. M. A. Hoefer, M. Sommacal, and T. J. Silva,听Propagation and control of nanoscale magnetic-droplet solitons,听. (reprint)
  53. D. Yan, J. J. Chang, C. Hamner, M. Hoefer, P. G. Kevrekidis, P. Engels, V. Achilleos, D. J. Frantzeskakis, and J. Cuevas,听Beating dark-dark solitons in Bose-Einstein condensates,听.
  54. M. A. Hoefer and M. Sommacal,听Propagating two-dimensional magnetic droplets,听. ()
  55. M. A. Hoefer and B. Ilan,听Dark solitons, dispersive shock waves, and transverse instabilities,听. (reprint)
  56. M. A. Hoefer, C. Hamner, J. J. Chang, and P. Engels,听Dark-dark solitons and modulational instability in miscible, two-component Bose-Einstein condensates,听. (reprint)
  57. C. Hamner, J. J. Chang, P. Engels, and M. A. Hoefer,听Generation of dark-bright soliton trains in superfluid-superfluid counterflow,听. (reprint)
  58. M. A. Hoefer and M. I. Weinstein,听Defect modes and homogenization of periodic Schr枚dinger operators,听. (reprint)
  59. A. Tovbis and M. A. Hoefer,听Semiclassical dynamics of quasi-one-dimensional attractive Bose-Einstein condensates,听. ()
  60. M. A. Hoefer, T. J. Silva, and M. W. Keller,听Theory for a dissipative droplet soliton excited by a spin torque nanocontact,听. (reprint)
  61. M. A. Hoefer and B. Ilan,听Theory of two-dimensional oblique dispersive shock waves in supersonic flow of a superfluid,听. (reprint)
  62. M. J. Ablowitz and M. A. Hoefer,听Dispersive shock waves,听.
  63. M. J. Ablowitz, D. E. Baldwin, and M. A. Hoefer,听Soliton generation and multiple phases in dispersive shock and rarefaction wave interaction,听. (reprint)
  64. M. A. Hoefer, P. Engels, and J. J. Chang,听Matter-wave interference in Bose-Einstein condensates: 听a dispersive hydrodynamic approach,. ()
  65. J. J. Chang, P. Engels, and M. A. Hoefer,听Formation of dispersive shock waves by merging and splitting Bose-Einstein condensates,. (reprint)
  66. M. A. Hoefer, T. J. Silva, and M. D. Stiles,听Model for a collimated spin-wave beam generated by a single-layer spin torque nanocontact,. (reprint)
  67. M. A. Hoefer, M. J. Ablowitz, and P. Engels,听Piston dispersive shock wave problem,听. (reprint)
  68. M. A. Hoefer and M. J. Ablowitz,听Interactions of dispersive shock waves,听. ()
  69. P. Engels, C. Atherton, and M. A. Hoefer,听Observation of Faraday waves in a Bose-Einstein condensate,听. (reprint)
  70. M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhard,听Dispersive and classical shock waves in Bose-Einstein condensates and gas dynamics,听. (reprint)
  71. M. A. Hoefer, M. J. Ablowitz, B. Ilan, M. R. Pufall, and T. J. Silva,听Theory of magnetodynamics induced by spin torque in perpendicularly magnetized thin films,听. (reprint)