For authors
Submission status

Archive (English)
   Volumes 113-119
   Volumes 93-112
      Volume 112
      Volume 111
      Volume 110
      Volume 109
      Volume 108
      Volume 107
      Volume 106
      Volume 105
      Volume 104
      Volume 103
      Volume 102
      Volume 101
      Volume 100
      Volume 99
      Volume 98
      Volume 97
      Volume 96
      Volume 95
      Volume 94
      Volume 93
VOLUME 94 (2011) | ISSUE 12 | PAGE 921
Hamiltonian form and solitary waves of the spatial Dysthe equations
The spatial Dysthe equations describe the envelope evolution of the free-surface and potential of gravity waves in deep waters. Their Hamiltonian structure and new invariants are unveiled by means of a gauge transformation to a new canonical form of the evolution equations. An accurate Fourier-type spectral scheme is used to solve for the wave dynamics and validate the new conservation laws, which are satisfied up to machine precision. Moreover, traveling waves are numerically constructed using the Petviashvili method. It is shown that their collision appears inelastic, suggesting the non-integrability of the Dysthe equations.