Geometry of Non-Linear Differential Equations, Backlund Transformations, and Solitons, Part A
By addebook • Oct 3rd, 2008 • Category: Mathematics •
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Geometry of Non-Linear Differential Equations, Backlund Transformations, and Solitons, Part A (Interdisciplinary Mathematics Series No. 12)
by Robert Hermann
Geometry of Non-Linear Differential Equations, Backlund Transformations, and Solitons, Part A (Interdisciplinary Mathematics Series No. 12)
By Robert Hermann
Publisher: Math Science Pr
Number Of Pages:
Publication Date: 1976-03
ISBN-10 / ASIN: 0915692163
ISBN-13 / EAN: 9780915692163
Binding: Paperback
Approximate Contents (CHAPTER TITLE / page number / keyword,keyword,keyword ) :
MAPPING ELEMENT SPACES AND SYSTEMS
1
differential form, PARTIAL DIFFERENTIAL EQUATIONS, vector fields
Mapping Element Jet Spaces
9
equivalence relation, algebraic geometry, differential equations
CauchyKowalewski Systems
20
formal power series, Cauchy data, differential equation
A Geometric and GroupTheoretic Interpretation
26
vector field, Pfaffian system, quantum field theory
MAYER SYSTEMS AND FOLIATIONS
65
Lie differential, ordinary differential equations, covering map
COMPLETE FAMILIES OF SOLUTIONS
81
Hamilton equations, complete family, family of solutions
Complete Families of Solution Manifolds
87
Pfaffian system, Cartan, SOLUTION MANIFOLDS
SOME GENERAL IDEAS OF GALOIS THEORY
91
Galois theory, Galois group, Lie group
LIE AND BACKLUND SYMMETRIES OF DIFFERENTIAL
147
linear differential operator, equivalence relation, equivalence class
The Lie Differential Form System
153
Sine-Gordon equation, integrability conditions, differential form system
THE PROLONGATION STRUCTURE OF ESTABROOK
165
Korteweg-de Vries equation, exterior algebra, differential ideal
Systems which Admit a Pseudoconservation
171
one-form, G-valued, Maurer-Cartan form
Lie Algebra Valued OneForms and Cartan
183
curvature forms, vector bundle, G-valued
The Bianchi Identity The Frobenius Condition
189
curvature forms, differential ideal, Korteweg-de Vries equation
BACKLUND TRANSFORMATIONS
207
Sine-Gordon equation, heat equation, homomorphisms
THE LAPLACEDARBOUX TRANSFORMATION LINEAR
217
differential invariants, gauge transformation, scalar-valued functions
The LaplaceDarboux Transform as a Linear
223
Klein-Gordon equation, Gauge Transformations, gauge group
HIGHER DERIVATIVE CONSERVATION LAWS
239
conservation law, SYMPLECTIC MANIFOLD, symplectic structure
A General Prolongation Process for Differential
251
CONSERVATION LAWS, Adfr 1, order mapping element
BACKLUND TRANSFORMATIONS AS CONNECTIONS
255
Goursat, EXTERIOR DIFFERENTIAL SYSTEMS, solution submanifolds
Backlund Transformations Determined
261
connection form, sin(y y, fiber space
Another TwoVariable Connection Approach
267
Sine-Gordon, dz A dt, EXTERIOR DIFFERENTIAL SYSTEMS
Systems Generated Algebraically by Zero
273
linear subspace, canonical form, TWO-FORM
Algebraic Study of Pairs of Skew Symmetric
281
skew-symmetric, bilinear forms, polynomial
DEFORMATIONS OF EXTERIOR DIFFERENTIAL
289
SINGULAR PERTURBATION, Group Representations, ORDINARY DIFFERENTIAL EQUATIONS
Singular Perturbation via the Riccati Equation
295
singular perturbation, real analytic, SUB(X
BIBLIOGRAPHY
305
vector-valued differential form, nonlinear wave, wave equation
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