Extended two dimensional equation for the description of nonlinear waves in gas-liquid mixture

Abstract

We consider a system of equations for the description of nonlinear waves in a liquid with gas bubbles. Taking into account high order terms with respect to a small parameter, we derive a new nonlinear partial differential equation for the description of density perturbations of mixture in the two-dimensional case. We investigate integrability of this equation using the Painlevé approach. We show that travelling wave reduction of the equation is integrable under some conditions on parameters. Some exact solutions of the equation derived are constructed. We also perform numerical investigation of the nonlinear waves described by the derived equation.

References in corpus (6)

• On one of methods for finding exact solutions of nonlinear differential equations
• Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation
• Equation for three-dimensional nonlinear waves in liquid with gas bubbles
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Cited by in corpus (1)

• The fifth-order partial differential equation for the description of the α+β Fermi-Pasta-Ulam model