Journal ArticleDOI
Korteweg‐deVries Equation and Generalizations. V. Uniqueness and Nonexistence of Polynomial Conservation Laws
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In this paper, the conservation laws derived in an earlier paper for the KortewegdeVries equation are proved to be the only ones of polynomial form, and an algebraic operator formalism is developed to obtain explicit formulas for them.Abstract:
The conservation laws derived in an earlier paper for the Korteweg‐deVries equation are proved to be the only ones of polynomial form. An algebraic operator formalism is developed to obtain explicit formulas for them.read more
Citations
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The soliton: A new concept in applied science
TL;DR: The term soliton has been coined to describe a pulselike nonlinear wave (solitary wave) which emerges from a collision with a similar pulse having unchanged shape and speed.
Journal ArticleDOI
Korteweg-devries equation and generalizations. VI. methods for exact solution
Journal ArticleDOI
The Korteweg–deVries Equation: A Survey of Results
TL;DR: A survey of results for the Korteweg-deVries equation can be found in this paper, including conservation laws, an alternate method for exact solution, soliton solutions, asymptotic behavior of solutions, Backlund transformation, and a nonlinear WKB method.
Journal ArticleDOI
The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
TL;DR: In this article, a trace identity based approach to Hamiltonian structures of integrable systems is proposed by making use of trace identity for a variety of isospectral problems that can be unified to one model ψx=Uψ.
References
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Journal ArticleDOI
Korteweg‐de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion
TL;DR: In this article, a variety of conservation laws and constants of motion for the Kortewegde Vries and related equations are derived for the Sturm-Liouville eigenvalue problem.
Journal ArticleDOI
Non-Linear Dispersive Waves
TL;DR: In this paper, a general theory for studying changes of a wave train governed by non-linear partial differential equations is developed for water waves and plasma dynamics, and the theory is developed using typical equations from these areas.
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