Numerical calculation of <i>N</i> -periodic wave solutions to coupled KdV–Toda-type equations
Yingnan Zhang, Xing‐Biao Hu, Jianqing Sun
2021Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences13 citationsDOIOpen Access PDF
Abstract
In this paper, we study the N -periodic wave solutions of coupled Korteweg–de Vries (KdV)–Toda-type equations. We present a numerical process to calculate the N -periodic waves based on the direct method of calculating periodic wave solutions proposed by Akira Nakamura. Particularly, in the case of N = 3, we give some detailed examples to show the N -periodic wave solutions to the coupled Ramani equation, the Hirota–Satsuma coupled KdV equation, the coupled Ito equation, the Blaszak–Marciniak lattice, the semi-discrete KdV equation, the Leznov lattice and a relativistic Toda lattice.
Topics & Concepts
Korteweg–de Vries equationToda latticeLattice (music)MathematicsType (biology)Mathematical analysisMathematical physicsPhysicsNonlinear systemQuantum mechanicsAcousticsEcologyIntegrable systemBiologyNonlinear Waves and SolitonsNonlinear Photonic SystemsAlgebraic structures and combinatorial models