1997/10/16 by R. P. Malik, Malik, R. P.
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #hep-th #nlin.SI #solv-int
paper · pdf · doi:10.48550/arxiv.solv-int/9710010
12 pages, latex, (no figures)
arxiv created 1997/10/16 · openalex publication_date 1997/10/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The dynamics of the highly nonlinear fifth order KdV-type equation is discussed in the framework of the Lagrangian and Hamiltonian formalisms. The symmetries of the Lagrangian produce three commuting conserved quantities that are found to be recursively related to one-another for a certain specific value of the power of nonlinearity. The above cited recursion relations are obeyed with a second Poisson bracket which sheds light on the integrability properties of the above nonlinear equation. It is shown that a Miura-type transformation can be made to obtain the fifth order mKdV-type equation from the fifth order KdV-type equation. The spatial dependence of the fields involved is, however, not physically interesting from the point of view of the solitonic solutions. As a consequence, it seems that the fifth order KdV- and mKdV-type equations are completely independent nonlinear evolution equations in their own right.