Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics

1. Front Matter

   Pages i-xxiv

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2. Poincare-Invariant Nonlinear Scalar Equations

   • W. I. Fushchich, W. M. Shtelen, N. I. Serov

   Pages 1-54

3. Systems of Poincare-invariant Nonlinear PDEs

   • W. I. Fushchich, W. M. Shtelen, N. I. Serov

   Pages 55-146

4. Euclid and Galilei Groups and Nonlinear PDEs for Scalar Fields

   • W. I. Fushchich, W. M. Shtelen, N. I. Serov

   Pages 147-198

5. Systems of PDEs Invariant Under Galilei Group

   • W. I. Fushchich, W. M. Shtelen, N. I. Serov

   Pages 199-276

6. Some Special Questions

   • W. I. Fushchich, W. M. Shtelen, N. I. Serov

   Pages 277-363

7. Back Matter

   Pages 364-435

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by spin or (spin s = 1/2) field equations is emphasized because their solutions can be used for constructing solutions of other field equations insofar as fields with any spin may be constructed from spin s = 1/2 fields. A brief account of the main ideas of the book is presented in the Introduction. The book is largely based on the authors' works [55-109, 176-189, 13-16, 7*-14*,23*, 24*] carried out in the Institute of Mathematics, Academy of Sciences of the Ukraine. References to other sources is not intended to imply completeness. As a rule, only those works used directly are cited. The authors wish to express their gratitude to Academician Yu.A. Mitropoi­ sky, and to Academician of Academy of Sciences of the Ukraine O.S. Parasyuk, for basic support and stimulation over the course of many years; to our cowork­ ers in the Department of Applied Studies, LA. Egorchenko, R.Z. Zhdanov, A.G. Nikitin, LV. Revenko, V.L Lagno, and I.M. Tsifra for assistance with the manuscript.

• Theoretical physics
• algebra
• calculus
• differential equation
• mathematical physics
• operator
• partial differential equation
• transformation

• Institute of Mathematics, Kiev, Ukraine

  W. I. Fushchich, W. M. Shtelen, N. I. Serov

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