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| by: Robert Hermann |
Geometry of Non-Linear Differential Equations, Backlund Transformations, and Solitons (Interdisciplinary Mathematics Series, No 14/Part B)
by: Robert Hermann
* Publisher: Math Science Pr
* Number Of Pages:
* Publication Date: 1976-06
* ISBN-10 / ASIN: 091569218X
* ISBN-13 / EAN: 9780915692187
* Binding: Paperback
*
CONTENTS: (CHAPTER TITLE/page number/CHAPTER KEYWORDS)
PROLONGATIONS OF DIFFERENTIAL EQUATIONS 1 partial differential equations, homomorphism, BACKLUND TRANSFORMATIONS The Traditional Backlund Transformation 7 PARTIAL DIFFERENTIAL EQUATIONS, Whitham, INDEPENDENT VARIABLES DIFFERENTIAL EQUATION SYSTEMS 13 involution, dependent variables, PARTIAL DIFFERENTIAL EQUATIONS Involutiveness Conditions for Two Second 21 Poisson bracket, involutiveness, DIFFERENTIAL EQUATIONS A Generalization of the Lax Equation 27 SYMPLECTIC MANIFOLDS, soliton, CONSTANTS OF MOTION Critical Point of a Constant of Motion 35 constants of motion, Lie group, one-parameter group THE MULTIPLE INTEGRAL DIFFERENTIAL FORM 49 Korteweg-de Vries equation, variational problem, DIFFERENTIAL FORM The Cartan Form for a Second Order Field 55 Korteweg-de Vries equation, Lagrange multiplier, one-form The EulerLagrange Exterior System for 65 Sine-Gordon equation, submanifold, conservation laws Variational Problems which have Two Indep 74 SYMPLECTIC MANIFOLDS, Lagrange multiplier, VECTOR SPACES Gradients of Infinite Dimensional Vector 80 Hamilton's equations, VECTOR SPACE, symmetric tensor The Formalism for the Kortewegde Vries 87 POISSON BRACKET, Hamilton's equation, Hamiltonian The Poisson Bracket Defined by Linear 93 Poisson bracket, conservation laws, Lagrangian derivates SYMMETRY GROUPS FOR ONEDIMENSIONAL 101 symplectic manifold, differential operator, Lie algebra Vector Fields Determined by RealValued 108 pseudopotential, soliton, Schrbdinger operators The Kortewegde Vries as a Linear Represen 115 LINEAR REPRESENTATION, Schrodinger equation, SCHRODINGER OPERATOR THE CONNECTION BETWEEN THE HAMILTON 121 HAMILTON'S EQUATIONS, CALCULUS OF VARIATIONS, vector space The Variational PrincipleHamiltonian Form 127 SINE-GORDON EQUATION, calculus of variations, HAMILTONIAN SYSTEM THE LIE ALGEBRA POISSONMOYAL BRACKET 133 Lie group, constants of motion, quantum mechanics The Kortewegde Vries Equation as a 139 KORTEWEG-DE VRIES EQUATION, Lax equation, zero-th order THE INVERSE SCATTERING TECHNIQUE 145 PSEUDOPOTENTIALS, differential equations, Lax equation Pfaffian Systems Determined by Linear 151 Sine-Gordon equations, vector bundle, PSEUDOPOTENTIALS The TwoComponent Linear Prolongation 158 PSEUDOPOTENTIAL, fiber bundle, differential forms ASYMPTOTIC BEHAVIOR OF THE SCHRODINGER 171 eigenvalues, ORDINARY DIFFERENTIAL EQUATIONS, CONSERVED CURRENTS Eigenvalue Problems for Linear Ordinary 177 eigenvalue, linear map, integral equation The Classical SturmLiouville Expansion 183 conserved current, perturbation expansion, cos Xx DEFORMATIONS OF PROLONGATION INFINI 191 formal power series, differential forms, singular perturbation CARTANS THEORY OF ALGEBRAIC EXTERIOR 205 linear subspace, linear map, linearly independent Regular Solution Subspaces 211 linear subspace, Pfaffian systems, regular solution A Calculation of the Cartan Characters 223 Cauchy characteristic vectors, formula 5.1, Cartan A SINGLE FIRST ORDER PARTIAL DIFFERENTIAL 229 ordinary differential equations, solution surface, surface of 2.1 The Cauchy Characteristic Vector Field 235 Cauchy problem, Cauchy data, hypersurface Singular Solutions of First Order Partial 245 Cauchy data, singular solution, coordinate system Lagranges Method of Variation of Parameters 253 VARIATION OF PARAMETERS, Cauchy characteristic, Lagrange THE CLASSICAL PROBLEM OF PFAFF 261 function group, Lagrangian subspaces, canonical coordinate FIRST ORDER SIMULTANEOUS DIFFERENTIAL 299 POISSON BRACKET, Cauchy characteristic vector, Cartan's CARTAN CHARACTERISTICS FOR EXTERIOR 309 tangent vectors, regular solution, solution element The GoursatCartan Algorithm 316 order partial differential, dy A dt The Cartan Generalized Cauchy Character 325 Pfaffian Systems, Differential Geometry, Lie Groups
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