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Direct and Inverse Methods in Nonlinear Evolution Equations
  • Language: en
  • Pages: 306

Direct and Inverse Methods in Nonlinear Evolution Equations

Many physical phenomena are described by nonlinear evolution equation. Those that are integrable provide various mathematical methods, presented by experts in this tutorial book, to find special analytic solutions to both integrable and partially integrable equations. The direct method to build solutions includes the analysis of singularities à la Painlevé, Lie symmetries leaving the equation invariant, extension of the Hirota method, construction of the nonlinear superposition formula. The main inverse method described here relies on the bi-hamiltonian structure of integrable equations. The book also presents some extension to equations with discrete independent and dependent variables. The different chapters face from different points of view the theory of exact solutions and of the complete integrability of nonlinear evolution equations. Several examples and applications to concrete problems allow the reader to experience directly the power of the different machineries involved.

The Painlevé Handbook
  • Language: en
  • Pages: 271

The Painlevé Handbook

Nonlinear differential or difference equations are encountered not only in mathematics, but also in many areas of physics (evolution equations, propagation of a signal in an optical fiber), chemistry (reaction-diffusion systems), and biology (competition of species). This book introduces the reader to methods allowing one to build explicit solutions to these equations. A prerequisite task is to investigate whether the chances of success are high or low, and this can be achieved without any a priori knowledge of the solutions, with a powerful algorithm presented in detail called the Painlevé test. If the equation under study passes the Painlevé test, the equation is presumed integrable. If ...

Register of Commissioned and Warrant Officers of the United States Naval Reserve
  • Language: en
  • Pages: 1478

Register of Commissioned and Warrant Officers of the United States Naval Reserve

  • Type: Book
  • -
  • Published: 1944
  • -
  • Publisher: Unknown

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California Public School Directory
  • Language: en
  • Pages: 804

California Public School Directory

  • Type: Book
  • -
  • Published: 1983
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  • Publisher: Unknown

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Transcript of the Enrollment Books
  • Language: en
  • Pages: 1082

Transcript of the Enrollment Books

  • Type: Book
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  • Published: 1958
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  • Publisher: Unknown

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The Official Catholic Directory for the Year of Our Lord ...
  • Language: en
  • Pages: 2508

The Official Catholic Directory for the Year of Our Lord ...

  • Type: Book
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  • Published: 2000
  • -
  • Publisher: Unknown

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Congressional Record
  • Language: en
  • Pages: 1338

Congressional Record

  • Categories: Law
  • Type: Book
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  • Published: 1959
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  • Publisher: Unknown

The Congressional Record is the official record of the proceedings and debates of the United States Congress. It is published daily when Congress is in session. The Congressional Record began publication in 1873. Debates for sessions prior to 1873 are recorded in The Debates and Proceedings in the Congress of the United States (1789-1824), the Register of Debates in Congress (1824-1837), and the Congressional Globe (1833-1873)

Federal Register
  • Language: en
  • Pages: 1340

Federal Register

  • Type: Book
  • -
  • Published: 1983-06-08
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  • Publisher: Unknown

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The Michigan Bar Journal
  • Language: en
  • Pages: 1750

The Michigan Bar Journal

  • Type: Book
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  • Published: 2003
  • -
  • Publisher: Unknown

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Index of Patents Issued from the United States Patent and Trademark Office
  • Language: en
  • Pages: 1736

Index of Patents Issued from the United States Patent and Trademark Office

  • Type: Book
  • -
  • Published: 1993
  • -
  • Publisher: Unknown

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