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Asymptotics of kink-kink interaction for sine-Gordon type equations. (English. Russian original) Zbl 1059.35119
Math. Notes 75, No. 4, 563-567 (2004); translation from Mat. Zametki 75, No. 4, 603-607 (2004).
Summary: We consider a class of semilinear wave equations with a small parameter \(\varepsilon\). The nonlinearity of \(F(u)\) is assumed to be such that the corresponding equation has an exact self-similar solution of kink type. For \(F(u)\), we obtain sufficient conditions for two kinks to interact (in the sense of the leading term of the asymptotics with respect to \(\varepsilon)\) in the same way as the kinks of the sine-Gordon equation.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35L70 Second-order nonlinear hyperbolic equations
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