Methods of Transformation Groups
نویسنده
چکیده
1. Continuous Transformation Groups 1.1. Local Transformation Groups 1.2. Lie Equations 1.3. Invariants 1.4. Invariant Manifolds 2. Invariant Differential Equations 2.1. The Continuation of Point Transformations 2.2. Defining Equation 2.3. Invariant and Partly Invariant Solutions 3. Tangential Transformations 3.1. Contact Transformations 3.2. Tangential Transformations of Finite and Infinite Orders 4. Conservation Laws 4.1. Noether Theorem 4.2. The Action of Connected Algebra 4.3. Examples 5. Bäcklund Transformations 6. Sine-Gordon Equation 7. Korteweg de Vries Equation and Lax Pairs 8. Hirota Transformation and Penleve Property 9. Method of Inverse Scattering Problem 10. Schrödinger Equation Glossary Bibliography Biographical Sketch
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