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      Separation of Variables and Exact Solutions to Nonlinear PDEs
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      Book

      Separation of Variables and Exact Solutions to Nonlinear PDEs

      DOI link for Separation of Variables and Exact Solutions to Nonlinear PDEs

      Separation of Variables and Exact Solutions to Nonlinear PDEs book

      Separation of Variables and Exact Solutions to Nonlinear PDEs

      DOI link for Separation of Variables and Exact Solutions to Nonlinear PDEs

      Separation of Variables and Exact Solutions to Nonlinear PDEs book

      ByAndrei D. Polyanin, Alexei I. Zhurov
      Edition 1st Edition
      First Published 2021
      eBook Published 20 September 2021
      Pub. Location New York
      Imprint Chapman and Hall/CRC
      DOI https://doi.org/10.1201/9781003042297
      Pages 401
      eBook ISBN 9781003042297
      Subjects Engineering & Technology, Mathematics & Statistics
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      Polyanin, A.D., & Zhurov, A.I. (2021). Separation of Variables and Exact Solutions to Nonlinear PDEs (1st ed.). Chapman and Hall/CRC. https://doi.org/10.1201/9781003042297

      ABSTRACT

      Separation of Variables and Exact Solutions to Nonlinear PDEs is devoted to describing and applying methods of generalized and functional separation of variables used to find exact solutions of nonlinear partial differential equations (PDEs). It also presents the direct method of symmetry reductions and its more general version. In addition, the authors describe the differential constraint method, which generalizes many other exact methods.

      The presentation involves numerous examples of utilizing the methods to find exact solutions to specific nonlinear equations of mathematical physics. The equations of heat and mass transfer, wave theory, hydrodynamics, nonlinear optics, combustion theory, chemical technology, biology, and other disciplines are studied.

      Particular attention is paid to nonlinear equations of a reasonably general form that depend on one or several arbitrary functions. Such equations are the most difficult to analyze. Their exact solutions are of significant practical interest, as they are suitable to assess the accuracy of various approximate analytical and numerical methods.

      The book contains new material previously unpublished in monographs. It is intended for a broad audience of scientists, engineers, instructors, and students specializing in applied and computational mathematics, theoretical physics, mechanics, control theory, chemical engineering science, and other disciplines.

      Individual sections of the book and examples are suitable for lecture courses on partial differential equations, equations of mathematical physics, and methods of mathematical physics, for delivering special courses and for practical training.

      TABLE OF CONTENTS

      chapter 1|90 pages

      Methods of Generalized Separation of Variables

      chapter 2|160 pages

      Methods of Functional Separation of Variables

      chapter 3|52 pages

      Direct Method of Symmetry Reductions. Weak Symmetries

      chapter 4|50 pages

      Method of Differential Constraints

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