Exact solutions of some nonlinear evolution equations using symbolic computations

DOI10.1016/S0898-1221(00)00161-9zbMath0956.35113MaRDI QIDQ1586283

R. Smith

Publication date: 13 November 2000

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

zbMATH Keywords

Kuramoto-Sivashinsky equationBurgers' equationnonlinear heat equationsymbolic computationsmodified KdV equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Solutions to PDEs in closed form (35C05) Software, source code, etc. for problems pertaining to partial differential equations (35-04)

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Cites Work

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• Using symbolic computation to exactly solve for the Bogoyavlenskii's generalized breaking soliton equation
• Generalized tanh method with symbolic computation and generalized shallow water wave equation
• Some global dynamical properties of the Kuramoto-Sivashinsky equations: nonlinear stability and attractors
• Second-order splitting combined with orthogonal cubic spline collocation method for the Kuramoto-Sivashinsky equation
• Some practical experience with the time integration of dissipative equations
• On the remarkable nonlinear diffusion equation (∂/∂x)[a (u+b)−2(∂u/∂x)−(∂u/∂t)=0]
• When Nonlinear Differential Equations are Equivalent to Linear Differential Equations
• A group analysis approach for a nonlinear differential system arising in diffusion phenomena
• Some Numerical Aspects of Computing Inertial Manifolds
• The partial differential equation u_t + uu_x = μ_xx
• On a quasi-linear parabolic equation occurring in aerodynamics