Stokes phenomena and monodromy deformation problem for nonlinear Schrodinger equation

Journal Article · Tue Jul 01 04:00:00 EDT 1986 · Int. J. Theor. Phys.; (United States)

DOI:https://doi.org/10.1007/BF00668722· OSTI ID:7083750

Chowdury, A R; Naskar, M

Following Flaschka and Newell, the inverse problem for Painleve IV is formulated with the help of similarity variables. The Painleve IV arises as the eliminant of the two second-order ordinary differential equations originating from the nonlinear Schrodinger equation. Asymptotic expansions are obtained near the singularities at zero and infinity of the complex eigenvalue plane. The corresponding analysis then displays the Stokes phenomena. The monodromy matrices connecting the solution Y /sub j/ in the sector S /sub j/ to that in S /sub j+1/ are fixed in structure by the imposition of certain conditions. It is then shown that a deformation keeping the monodromy data fixed leads to the nonlinear Schrodinger equation. While Flaschka and Newell did not make any absolute determination of the Stokes parameters, the present approach yields the values of the Stokes parameters in an explicit way, which in turn can determine the matrix connecting the solutions near zero and infinity. Finally, it is shown that the integral equation originating from the analyticity and asymptotic nature of the problem leads to the similarity solution previously determined by Boiti and Pampinelli.

• Research Organization: Jadavpur Univ., Calcutta
• OSTI ID: 7083750
• Journal Information: Int. J. Theor. Phys.; (United States), Journal Name: Int. J. Theor. Phys.; (United States) Vol. 25:7; ISSN IJTPB
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
ASYMPTOTIC SOLUTIONS
BOUNDARY CONDITIONS
BOUNDARY-VALUE PROBLEMS
DEFORMATION
DIFFERENTIAL EQUATIONS
EQUATIONS
INVERSE SCATTERING PROBLEM
MATRICES
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
SCHROEDINGER EQUATION
SINGULARITY
STOKES PARAMETERS
WAVE EQUATIONS