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Approximate symmetry reduction method and the application of hyperbolic functions

Author: ZhangZuo
Tutor: ZhangShunLi
School: Northwestern University
Course: Applied Mathematics
Keywords: KP equation K (n, l) Equation Homotopy model Disturbance Law
CLC: O175.27
Type: Master's thesis
Year: 2011
Downloads: 35
Quote: 0
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Abstract


With the advances in modern science and technology and development, has gradually become nonlinear science disciplines and interdisciplinary cross each key , and for modern technology played a decisive role in the promotion and for industrial production and technological innovation provides a theoretical support . Many physics and other disciplines in question are often in the form of nonlinear partial differential equations to describe , therefore , study the various disciplines within the nonlinear problem is becoming increasingly important , the paper introduces a method of approximate reduction and dual Qu function method for the approximate solution of the given equation with the exact solution were studied. The first chapter introduces the history of the development approximate symmetry method , which raises questions about solving perturbation perturbation theorem, combined with a brief introduction to perturbation theorems for items with a weak disturbance approximate symmetry symmetry reduction method for the general case does not contain the small parameter perturbation equation describes the homotopy analysis method and combining this method describes the approximate homotopy symmetry method . Second, the introduction of the hyperbolic function method and the historical background of this method for the study of a large class of exact solutions of evolution equations significance. The second chapter describes the expansion of the hyperbolic function method and the introduction of the KP equation , the introduction of the concept of traveling wave solutions and balance equations method , and thus the hyperbolic function method further extension , the use of extension hyperbolic function method , further obtained on a variety of exact solutions of the KP equation . Chapter III describes the K (n, m) equation with damping term and thus leads to a K (n, 1) equation model using linear homotopy damping K (n, 1) and using perturbation equations rewrite the law be translated into equations, and methods were applied symmetry of the obtained direct method for reduction of equations and the approximate solution obtained , and the results of the two methods for each derivation .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Partial Differential Equations > Hyperbolic equations
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