Solitons on moving space curves
Author:
- 1 August 1977
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 18 (8) , 1654-1661
Abstract
It is shown that the motion of certain types of helical space curves may be related to the sine–Gordon equation and to the Hirota equation (and consequently to the nonlinear Schrödinger equation and to the modified Korteweg–de Vries equation). The intrinsic equations that govern the motion of space curves are shown to provide the various linear equations that have been introduced to solve these evolution equations by inverse scattering methods.Keywords
This publication has 21 references indexed in Scilit:
- Nonlinear evolution equations solvable by the inverse spectral transform.—IIl Nuovo Cimento B (1971-1996), 1976
- Prolongation structures of nonlinear evolution equationsJournal of Mathematical Physics, 1975
- Four examples of the inverse method as a canonical transformationJournal of Mathematical Physics, 1975
- The Inverse Scattering Transform‐Fourier Analysis for Nonlinear ProblemsStudies in Applied Mathematics, 1974
- Bäcklund transformations for certain nonlinear evolution equationsJournal of Mathematical Physics, 1974
- Bäcklund Transformation for Solutions of the Korteweg-de Vries EquationPhysical Review Letters, 1973
- Nonlinear-Evolution Equations of Physical SignificancePhysical Review Letters, 1973
- Integrals of nonlinear equations of evolution and solitary wavesCommunications on Pure and Applied Mathematics, 1968
- Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of MotionJournal of Mathematical Physics, 1968
- Method for Solving the Korteweg-deVries EquationPhysical Review Letters, 1967