Weakly Nonlocal Solitary Waves in a Singularly Perturbed Korteweg-De Vries Equation

A fifth-order Korteweg–de Vries equation is considered, where the fifth-order derivative term is multiplied by a small parameter. It is known that solitary wave solutions of this model equation are nonlocal in that the central core of the wave is accompanied by copropagating trailing oscillations. Here, using the techniques of exponential asymptotics, these solutions are reexamined and it is established that they form a one-parameter family characterized by the phase shift of the trailing oscillations. Explicit asymptotic formula relating the oscillation amplitude to the phase shift are obtained.

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