On approximate symmetry and approximate solutions of the nonlinear wave equation with a small parameter. (English) Zbl 0711.35086

Summary: The concept of approximate symmetry is introduced. We describe all nonlinearities F(u) with which the nonlinear wave equation \(\square u+\lambda u^ 3+\epsilon F(u)=0\) with a small parameter \(\epsilon\) is approximately scale and conformally invariant. Some approximate solutions of wave equations in question are obtained using the approximate symmetry.


35L70 Second-order nonlinear hyperbolic equations
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