Korteweg-de Vries and nonlinear Schröginger [i.e. Schrödinger] equations : qualitative theory / Peter E. Zhidkov

Author(s): Zhidkov, Peter E., 1956-
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Subjects: Korteweg-de Vries equation
Schrödinger equation
Formats: Print
Material Type: Books
Language: English
Audience: Unspecified
Published: Berlin ; New York : Springer, c2001
Series: Lecture notes in mathematics 1756
Lecture notes in mathematics (Springer-Verlag) 1756
LC Classification: Q, QA
Physical Description: 146 p. ; 24 cm
Table of Contents: Introduction 1
Notation 5
Ch. 1. Evolutionary equations. Results on existence 9
1.1. The (generalized) Korteweg-de Vries equation (KdVE) 10
1.2. The nonlinear Schrodinger equation (NLSE) 26
1.3. On the blowing up of solutions 36
1.4. Additional remarks 37
Ch. 2. Stationary problems 39
2.1. Existence of solutions. An ODE approach 42
2.2. Existence of solutions. A variational method 49
2.3. The concentration-compactness method of P. L. Lions 56
2.4. On Basis properties of systems of solutions 62
2.5. Additional remarks 76
Ch. 3. Stability of solutions 79
3.1. Stability of soliton-like solutions 80
3.2. Stability of kinks for the KdVE 90
3.3. Stability of solutions of the NLSE nonvanishing as 94
3.4. Additional remarks 103
Ch. 4. Invariant measures 105
4.1. On Gaussian measures in Hilbert spaces 107
4.2. An invariant measure for the NLSE 118
4.3. An infinite series of invariant measures for the KdVE 124
4.4. Additional remarks 135
Bibliography 137
Index 147
Alternate Titles: Portion of title: Korteweg de Vries and nonlinear Schrödinger equations
Notes: LCCN: 2001020978
ISBN: 3540418334 (pbk. : alk. paper)
Includes bibliographical references (p. [137]-146) and index
OCLC Number: 46640669
ISBN/ISSN: 3540418334
0075-8434