Equation admitting linearization and describing waves in dissipative media with modular, quadratic, and quadratically cubic nonlinearities

DOI10.1134/S1064562416060053zbMath1362.35080MaRDI QIDQ521432

O. V. Rudenko

Publication date: 11 April 2017

Published in: Doklady Mathematics (Search for Journal in Brave)

zbMATH Keywords

formation of singularitiesdissipative shock wavescollision of two single pulses

Mathematics Subject Classification ID

Solitary waves in solid mechanics (74J35) Soliton solutions (35C08)

Related Items (17)

On a New Type of Periodic Fronts in Burgers Type Equations with Modular Advection ⋮ On front motion in a Burgers-type equation with quadratic and modular nonlinearity and nonlinear amplification ⋮ Inhomogeneous Burgers equation with modular nonlinearity: excitation and evolution of high-intensity waves ⋮ Wave excitation in a dissipative medium with a double quadratically-modular nonlinearity: a generalization of the inhomogeneous Burgers equation ⋮ One-dimensional model of KZ-type equations for waves in the focal region of cubic and quadratically-cubic nonlinear media ⋮ Stationary waves in a bimodular rod of finite radius ⋮ Existence of solutions of a system of two ordinary differential equations with a modular-cubic type nonlinearity ⋮ Asymptotic solution of coefficient inverse problems for Burgers-type equations ⋮ On a periodic inner layer in the reaction-diffusion problem with a modular cubic source ⋮ Single shock and periodic sawtooth-shaped waves in media with non-analytic nonlinearities ⋮ On the motion, amplification, and blow-up of fronts in Burgers-type equations with quadratic and modular nonlinearity ⋮ Solution with an inner transition layer of a two-dimensional boundary value reaction-diffusion-advection problem with discontinuous reaction and advection terms ⋮ The existence and asymptotic stability of periodic solutions with an interior layer of Burgers type equations with modular advection ⋮ Development of methods of asymptotic analysis of transition layers in reaction-diffusion-advection equations: theory and applications ⋮ Strong nonlinearity, anisotropy, and solitons in a lattice with holonomic constraints ⋮ Asymptotic stability of viscous shocks in the modular Burgers equation ⋮ Asymptotic solution of the boundary control problem for a Burgers-type equation with modular advection and linear gain

Cites Work

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• Self-similar solutions of a Burgers-type equation with quadratically cubic nonlinearity
• Quadratically cubic Burgers' equation as exactly solvable model of mathematical physics
• Propagation of nonlinear acoustic waves in bimodular media with linear dissipation
• Waves and structures in nonlinear nondispersive media. General theory and applications to nonlinear acoustics.
• Self-similar waves in media with bimodular elastic nonlinearity and relaxation

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