Exact solutions and generalized conditional symmetries to (1 + 1)-dimensional reaction-diffusion equations

Huabing Jia; Wei Xu; Hongxian Zhou

doi:10.1016/j.cnsns.2009.12.014

Exact solutions and generalized conditional symmetries to (1 + 1)-dimensional reaction-diffusion equations

Huabing Jia, Wei Xu, Hongxian Zhou

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

For the (1 + 1)-dimensional nonlinear reaction-diffusion equations, we obtain conditions under which the equations admit a class of second-order generalized conditional symmetries. η (u) = u_xx - H (u) u_x² - A (u) u_x - B (u). and first-order sign-invariants J (u) = u_t - F (u) u_x² - P (u) u_x - T (u) on the solutions u (x, t). Several different generalized conditional symmetries and first-order sign-invariants for equations are presented. Exact solutions to the resulting equations corresponding to the generalized conditional symmetries and first-order sign-invariants are constructed.

Original language	English
Pages (from-to)	3367-3378
Number of pages	12
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	15
Issue number	11
DOIs	https://doi.org/10.1016/j.cnsns.2009.12.014
State	Published - Nov 2010

Keywords

Exact solution
Generalized conditional symmetries
Reaction-diffusion equation
Sign-invariant

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10.1016/j.cnsns.2009.12.014

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abstract = "For the (1 + 1)-dimensional nonlinear reaction-diffusion equations, we obtain conditions under which the equations admit a class of second-order generalized conditional symmetries. η (u) = uxx - H (u) ux2 - A (u) ux - B (u). and first-order sign-invariants J (u) = ut - F (u) ux2 - P (u) ux - T (u) on the solutions u (x, t). Several different generalized conditional symmetries and first-order sign-invariants for equations are presented. Exact solutions to the resulting equations corresponding to the generalized conditional symmetries and first-order sign-invariants are constructed.",

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T1 - Exact solutions and generalized conditional symmetries to (1 + 1)-dimensional reaction-diffusion equations

AU - Jia, Huabing

AU - Xu, Wei

AU - Zhou, Hongxian

PY - 2010/11

Y1 - 2010/11

N2 - For the (1 + 1)-dimensional nonlinear reaction-diffusion equations, we obtain conditions under which the equations admit a class of second-order generalized conditional symmetries. η (u) = uxx - H (u) ux2 - A (u) ux - B (u). and first-order sign-invariants J (u) = ut - F (u) ux2 - P (u) ux - T (u) on the solutions u (x, t). Several different generalized conditional symmetries and first-order sign-invariants for equations are presented. Exact solutions to the resulting equations corresponding to the generalized conditional symmetries and first-order sign-invariants are constructed.

AB - For the (1 + 1)-dimensional nonlinear reaction-diffusion equations, we obtain conditions under which the equations admit a class of second-order generalized conditional symmetries. η (u) = uxx - H (u) ux2 - A (u) ux - B (u). and first-order sign-invariants J (u) = ut - F (u) ux2 - P (u) ux - T (u) on the solutions u (x, t). Several different generalized conditional symmetries and first-order sign-invariants for equations are presented. Exact solutions to the resulting equations corresponding to the generalized conditional symmetries and first-order sign-invariants are constructed.

KW - Exact solution

KW - Generalized conditional symmetries

KW - Reaction-diffusion equation

KW - Sign-invariant

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DO - 10.1016/j.cnsns.2009.12.014

M3 - 文章

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SN - 1007-5704

VL - 15

SP - 3367

EP - 3378

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

IS - 11

ER -

Exact solutions and generalized conditional symmetries to (1 + 1)-dimensional reaction-diffusion equations

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Keywords

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