Algebraic approaches to partial differential equations / Xiaoping Xu.

Format:

Book

Author/Creator:

Xu, Xiaoping (Mathematician), author.

Contributor:

Benjamin Franklin Library Fund.

Language:

English

Subjects (All):

Differential equations, Partial.

Physical Description:

xxiv, 394 pages ; 25 cm

Place of Publication:

Heidelberg ; New York : Springer, [2013]

Summary:

This book presents the various algebraic techniques for solving partial differential equations to yield exact solutions, techniques developed by the author in recent years and with emphasis on physical equations such as: the Maxwell equations, the Dirac equations, the KdV equation, the KP equation, the nonlinear Schrödinger equation, the Davey and Stewartson equations, the Boussinesq equations in geophysics, the Navier-Stokes equations and the boundary layer problems. In order to solve them, I have employed the grading technique, matrix differential operators, stable-range of nonlinear terms, moving frames, asymmetric assumptions, symmetry transformations, linearization techniques and special functions. The book is self-contained and requires only a minimal understanding of calculus and linear algebra, making it accessible to a broad audience in the fields of mathematics, the sciences and engineering. Readers may find the exact solutions and mathematical skills needed in their own research.

Contents:

1. First-order ordinary differential equations

2. Higher order ordinary differential equations

3. Special functions

4. First-order of linear equations

5. Nonlinear scalar equations

6. Nonlinear Schrödinger and Davey-Stewartson equations

7. Dynamic convection in a sea

8. Boussinesq equations in geophyics

9. Navier-Stokes equations

10. Classical boundary layer problems.

Notes:

Includes bibliographical references (pages 385-391) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Benjamin Franklin Library Fund.

ISBN:

3642368735

9783642368738

OCLC:

828494494

Publisher Number:

99954901416