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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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