Integrability, conservation laws and solitons of a many-body dynamical system associated with the half-wave maps equation
@article{Matsuno2021IntegrabilityCL, title={Integrability, conservation laws and solitons of a many-body dynamical system associated with the half-wave maps equation}, author={Yoshimasa Matsuno}, journal={Physica D: Nonlinear Phenomena}, year={2021} }
2 Citations
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References
SHOWING 1-10 OF 43 REFERENCES
Multi-solitons of the half-wave maps equation and Calogero–Moser spin–pole dynamics
- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2020
We consider the half-wave maps (HWM) equation which provides a continuum description of the classical Haldane–Shastry spin chain on the real line. We present exact multi-soliton solutions of this…
DYNAMICS OF INTERACTING ALGEBRAIC SOLITONS
- Physics, Mathematics
- 1995
A survey is made which highlights recent topics on the dynamics of algebraic solitons, which are exact solutions to a certain class of nonlinear integrodifferential evolution equations. The model…
Exactly solvable eigenvalue problems for a nonlocal nonlinear Schrödinger equation
- Mathematics, Physics
- 2002
The linear spectral problem is studied for a nonlocal nonlinear Schrodinger equation describing envelope waves in a stratified fluid of great depth. Two examples of the potentials are presented which…
The fascinating world of the Landau–Lifshitz–Gilbert equation: an overview
- PhysicsPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2011
An exciting recent development is that the spin torque effect in nanoferromagnets is described by a generalization of the LLG equation that forms a basic dynamical equation in the field of spintronics.
A Short Primer on the Half-Wave Maps Equation
- Mathematics
- 2018
We review the current state of results about the half-wave maps equation on the domain $\mathbb{R}^d$ with target $\mathbb{S}^2$. In particular, we focus on the energy-critical case $d=1$, where we…
Benjamin-Ono and Intermediate Long Wave Equations: Modeling, IST and PDE
- MathematicsNonlinear Dispersive Partial Differential Equations and Inverse Scattering
- 2019
This survey article is focused on two asymptotic models for internal waves, the Benjamin-Ono (BO) and Intermediate Long Wave (ILW) equations that are integrable by inverse scattering techniques…
A direct proof of the N-soliton solution of the Benjamin-Ono equation by means of Jacobi's formula
- Mathematics
- 1988
A direct proof of the, N -soliton solution of the Benjamin-Ono (BO) equation is presented within the framework of the theory of determinants. It is shown that the bilinear equation for the BO N…
A Cauchy problem for the nonlocal nonlinear Schrödinger equation
- Mathematics
- 2004
A Cauchy problem for the nonlocal nonlinear Schrodinger equation is formulated by means of the inverse scattering transform (IST) method. A closed system of IST equations for the Jost functions is…