It is shown that in a particular case of the small amplitude waves, a solution in the form of a two-breather molecule for the nonlinear Klein-Gordon equation coincides with the vector 0\pi pulse of the self-induced transparency which is presented under less stringent conditions compared to the same solution of this equation obtained earlier. leads to a system of linear algebraic equations of the form Ax b with non-linear differential equations one arrives at a system of non-linear equations, which cannot be solved by elementary elimination methods. The obtained solution coincides with the solutions of the two-breather molecule found in a number of well-known equations from different areas of physics. One breather oscillated with the sum, and the other with the difference of frequencies and wave numbers. For lecture courses that cover the classical theory of nonlinear differential equations associated with Poincare and Lyapunov and introduce the student to. An explicit analytical solution of a nonlinear wave equation in the form of a two-breather molecule was obtained. Find differential equations satisfied by a given function: differential equations sin 2x.
Using the slowly varying envelope approximation and the generalized perturbative reduction method, the nonlinear wave equation was transformed to coupled nonlinear Schrodinger equations for auxiliary functions. Solve a nonlinear equation: f'(t) f(t)2 + 1. In two particular cases, this equation was reduced to the Sine-Gordon equation and the Born-Infeld equation. Here, various methods of solving and approximating linear and. A nonlinear wave equation that describes different nonlinear effects in various fields of research was considered. Nonlinear differential equations arise as mathematical models of various phenom- ena.
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