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Solitons and modulation theory

2004

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Asymptotic Solitons For A Third-Order Kortweg-De Vries Equation, Tim Marchant Dec 2003

Asymptotic Solitons For A Third-Order Kortweg-De Vries Equation, Tim Marchant

Tim Marchant

Solitary wave interaction for a higher-order version of the Korteweg–de Vries (KdV) equation is considered. The equation is obtained by retaining third-order terms in the perturbation expansion, where for the KdV equation only first-order terms are retained. The third-order KdV equation can be asymptotically transformed to the KdV equation, if the third-order coefficients satisfy a certain algebraic relationship. The third-order two-soliton solution is derived using the transformation. The third-order phase shift corrections are found and it is shown that the collision is asymptotically elastic. The interaction of two third-order solitary waves is also considered numerically. Examples of an elastic ...