Instabilities of multiphase wave trains in coupled nonlinear Schrödinger equations: A bisymplectic framework

2005 ◽  
Vol 46 (8) ◽  
pp. 082701 ◽  
Author(s):  
F. E. Laine-Pearson
Keyword(s):  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Coupled Nonlinear Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Wave Trains ◽  
Coupled Nonlinear Schrodinger Equations

ANALYTICAL SOLUTIONS OF COUPLED NONLINEAR SCHRODINGER EQUATIONS FOR TWO NON LINEARLY INTERACTING STOKES WAVE TRAINS OVER INFINITE DEPTH

2021 ◽  
Vol 10 (3) ◽  
pp. 1137-1144
Author(s):  
S. Manna ◽  
A.K. Dhar
Keyword(s):  
Analytical Solutions ◽  
Nonlinear Schrödinger Equations ◽  
Stokes Wave ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Coupled Nonlinear Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Wave Trains ◽  
Coupled Nonlinear Schrodinger Equations

An attempt to find the exact analytical solutions of the two coupled nonlinear Schrodinger equations of 3rd order occurring from the oblique interaction of two capillary gravity wave trains in the case of crossing sea states in deep water is the main premise of the present paper. The solutions obtained here are due to the nonlinear interaction of two Stokes wave trains in one spatial dimension. Graphs have been plotted to investigate the influence of capillarity on the amplitudes of such wave trains. From 3D figures it has been observed that the capillarity has diminishing influence on the amplitudes of the either wave packet.

scholarly journals Quasi-periodic solutions of the coupled nonlinear Schrödinger equations

1995 ◽  
Vol 451 (1943) ◽  
pp. 685-700 ◽  
Keyword(s):  
Periodic Solutions ◽  
Nonlinear Schrödinger Equations ◽  
Integrable Case ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Coupled Nonlinear Schrödinger Equations ◽  
Fibre Optics ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Coupled Nonlinear Schrodinger Equations

We consider travelling periodic and quasi-periodic wave solutions of a set of coupled nonlinear Schrödinger equations. In fibre optics these equations can be used to model single mode fibres under the action of cross-phase modulation, with weak birefringence. The problem is reduced to the ‘1:2:1’ integrable case of the two-particle quartic potential. A general approach for finding elliptic solutions is given. New solutions which are associated with two-gap Treibich-Verdier potentials are found. General quasi-periodic solutions are given in terms of two dimensional theta functions with explicit expressions for frequencies in terms of theta constants. The reduction of quasi-periodic solutions to elliptic functions is discussed.

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