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NLS equation; solitary waves; asymptotic transformation; elastic and inelastic collisions; higher-order phase and coordinate shifts
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Solitary Wave Interaction For A Higher-Order Nonlinear Schrodinger Equation, Tim Marchant
Solitary Wave Interaction For A Higher-Order Nonlinear Schrodinger Equation, Tim Marchant
Tim Marchant
Solitary wave interaction for a higher-order version of the nonlinear Schrödinger (NLS) equation is examined. An asymptotic transformation is used to transform a higher-order NLS equation to a higher-order member of the NLS integrable hierarchy, if an algebraic relationship between the higher-order coefficients is satisfied. The transformation is used to derive the higher-order one- and two-soliton solutions; in general, the N-soliton solution can be derived. It is shown that the higher-order collision is asymptotically elastic and analytical expressions are found for the higher-order phase and coordinate shifts. Numerical simulations of the interaction of two higher-order solitary waves are also performed. …