Derives dispersive-dissipative estimates for a general class of wave-type equations including the viscous Boussinesq, relating phase function geometry and frequency degeneracies to decay rates influenced by dissipation.
On the asymptotic reduction to the multidimensional nonlinear Schrodinger equation
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abstract
The problem on the asymptotics for the solution of multidimensional nonlinear Boussinesq equation with respect to a small parameter $\ve$ is considered. The asymptotic expansion of the solution of this problem with respect to $\ve\to0$ for long times $t\sim {\cal O}(\ve^{-2})$ is constructed and justified. The leading terms of the asymptotic solution are defined from the multidimensional nonlinear Schrodinger equation and from the linear homogeneous wave equation.
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math.AP 1years
2026 1verdicts
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Dispersive-Dissipative estimates for Boussinesq and other generalized wave equations
Derives dispersive-dissipative estimates for a general class of wave-type equations including the viscous Boussinesq, relating phase function geometry and frequency degeneracies to decay rates influenced by dissipation.