A Generalized Auxiliary Equation Method for the Quadratic Nonlinear KG Equation
Applied Mechanics and Materials, 2013A generalized auxiliary equation method with symbolic computation is used to construct more general exact solutions of the quadratic nonlinear Klein-Gordon (KG) equation. As a result, new and more general solutions are obtained. It is shown that the generalized auxiliary equation method provides a more powerful mathematical tool for solving nonlinear ...
Sheng Zhang, Bo Xu, Ao Xue Peng
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An auxiliary equation method for obtaining superconvergent finite‐element approximations
Communications in Applied Numerical Methods, 1992AbstractA finite‐element method is developed which improves accuracy and yields superconvergent approximations to two‐dimensional elliptic boundary‐value problems on a union of square bilinear elements. This method employs an auxiliary equation which is derived using a Taylor series analysis on the discrete formula obtained from a Galerkin finite ...
Johnson, Richard W. +1 more
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The extended auxiliary equation method for the KdV equation with variable coefficients
Chinese Physics B, 2011This paper applies an extended auxiliary equation method to obtain exact solutions of the KdV equation with variable coefficients. As a result, solitary wave solutions, trigonometric function solutions, rational function solutions, Jacobi elliptic doubly periodic wave solutions, and nonsymmetrical kink solution are obtained.
Lan-Fang Shi +2 more
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A generalized auxiliary equation method and its applications
Nonlinear Dynamics, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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New exact solutions for mCH and mDP equations by auxiliary equation method
Applied Mathematics and Computation, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Bengong +2 more
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Reinterpretation of the auxiliary differential equation method for FDTD
IEEE Microwave and Wireless Components Letters, 2002The auxiliary differential equation method used for treating Lorentz media with the FDTD algorithm is reinterpreted to reduce computer memory requirements while maintaining full time synchronism. This new formulation enables us to save up to 20% of computer memory when compared to the previous approach.
Y. Takayama, W. Klaus
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A new auxiliary equation method for finding travelling wave solutions to KdV equation
Applied Mathematics and Mechanics, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pang, Jing, Bian, Chun-quan, Chao, Lu
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A note on the auxiliary equation method for solving nonlinear partial differential equations
Physics Letters A, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Chunping, Liu, Xiaoping
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New extended auxiliary equation method and its applications to nonlinear Schrödinger-type equations
Optik, 2016Abstract A new extended auxiliary equation method has been applied to construct many new types of Jacobi elliptic function solutions of nonlinear partial differential equations (PDEs) in mathematical physics. The effectiveness of this method is demonstrated by applications to three nonlinear PDEs, namely, the (2+1)-dimensional nonlinear cubic–quintic
E.M.E. Zayed, K.A.E. Alurrfi
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Exact Travelling Wave Solutions of the Nonlinear Evolution Equations by Auxiliary Equation Method
Zeitschrift für Naturforschung A, 2015Abstract The auxiliary equation method presents wide applicability to handling nonlinear wave equations. In this article, we establish new exact travelling wave solutions of the nonlinear Zoomeron equation, coupled Higgs equation, and equal width wave equation.
Akbulut, ARZU +2 more
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