Numerical analysis of soliton solutions of the modified Korteweg–de Vries–sine-Gordon equation

S. P. Popov

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 3, pp. 435-445

Résumé

Multisoliton solutions of the modified Korteweg–de Vries–sine-Gordon equation (mKdV-SG) are found numerically by applying the quasi-spectral Fourier method and the fourth-order Runge–Kutta method. The accuracy and features of the approach are determined as applied to problems with initial data in the form of various combinations of perturbed soliton distributions. Three-soliton solutions are obtained, and the generation of kinks, breathers, wobblers, perturbed kinks, and nonlinear oscillatory waves is studied.

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