Finite-gap solutions of the real modified Korteweg-de Vries equation
DOI10.1134/S0040577924070122zbMATH Open1548.37105MaRDI QIDQ6632262
Aleksandr Olegovich Smirnov, I. V. Anisimov
Publication date: 4 November 2024
Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)
Cites Work
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- Tangential polynomials and elliptic solitons
- Elliptic solutions of the Korteweg-de Vries equation
- Hill's operator with finitely many gaps
- Reduction of theta functions and elliptic finite-gap potentials
- Finite-gap elliptic solutions of the KdV equation
- The Heun equation and the Calogero-Moser-Sutherland system. I: The Bethe ansatz method
- On the transformation of linear differential equations
- Treibich-Verdier potentials and the stationary (m)KdV hierarchy
- Matrix finite-zone operators
- On the link between the Sparre equation and Darboux-Treibich-Verdier equation
- Finite-gap solutions of the Fuchsian equations
- The Heun equation and the Darboux transformation
- Isospectral deformations of elliptic potentials
- NON-LINEAR EQUATIONS OF KORTEWEG-DE VRIES TYPE, FINITE-ZONE LINEAR OPERATORS, AND ABELIAN VARIETIES
- On a class of elliptic potentials of the Dirac operator
- Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion
- On a linear equation.
- On the equation \[ \frac{d^2y}{dx^2}+\left[2\nu\,\frac{k^2\text{sn\,}x\text{cn\, }x} {\text{dn\,}x} +2\nu_1\;\frac{\text{sn\,}x\text{dn\,}x}{\text{cn\,}x} 2\nu_2\frac{\text{cn\,}x\text{dn\,}x}{\text{sn\,}x}\right]\;\frac{dy}{dx} \] \[ =\left[\frac{1}{\text{sn\,}^2x}(n_3 \nu_2)(n_3+\nu_2+1)+\frac{\text{dn\,}^2x}{\text{cn\,}^2x}(n_2 \nu_1)(n_2+\nu_1+1)\right. \] \[ \left.+\frac{k^2\text{cn}^2x}{\text{dn}^2x}\,(n_1 \nu)(n_1+\nu+1) +k^2\text{sn}^2x(n+\nu+\nu_1+\nu_2)(n \nu \nu_1 \nu_2+1)+h\right]y. \]
- Vector form of Kundu-Eckhaus equation and its simplest solutions
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