The $$\text{m}$$KdV-type equations related to $$A_5^{(1)}$$ and $$A_5^{(2)}$$ Kac–Moody algebras

2021 ◽  
Vol 207 (2) ◽  
pp. 604-625
Author(s):  
V. S. Gerdjikov ◽  
D. M. Mladenov ◽  
A. A. Stefanov ◽  
S. K. Varbev
Keyword(s):  
Kdv Type Equations

scholarly journals Integrability of Riemann-Type Hydrodynamical Systems and Dubrovin’s Integrability Classification of Perturbed KdV-Type Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1077
Author(s):  
Yarema A. Prykarpatskyy
Keyword(s):  
Conservation Laws ◽  
Hamiltonian Structure ◽  
Necessary Condition ◽  
Type Representation ◽  
Infinite Hierarchy ◽  
Polynomial Coefficients ◽  
Kdv Type Equations ◽  
Special Case

Dubrovin’s work on the classification of perturbed KdV-type equations is reanalyzed in detail via the gradient-holonomic integrability scheme, which was devised and developed jointly with Maxim Pavlov and collaborators some time ago. As a consequence of the reanalysis, one can show that Dubrovin’s criterion inherits important parts of the gradient-holonomic scheme properties, especially the necessary condition of suitably ordered reduction expansions with certain types of polynomial coefficients. In addition, we also analyze a special case of a new infinite hierarchy of Riemann-type hydrodynamical systems using a gradient-holonomic approach that was suggested jointly with M. Pavlov and collaborators. An infinite hierarchy of conservation laws, bi-Hamiltonian structure and the corresponding Lax-type representation are constructed for these systems.

scholarly journals Singular vectors and conservation laws of quantum KdV type equations

1992 ◽  
Vol 278 (1-2) ◽  
pp. 79-84 ◽  
Author(s):  
P. Di Francesco ◽  
P. Mathieu
Keyword(s):  
Conservation Laws ◽  
Singular Vectors ◽  
Kdv Type Equations

scholarly journals A hybrid LDG-HWENO scheme for KdV-type equations

2016 ◽  
Vol 313 ◽  
pp. 754-774 ◽  
Author(s):  
Dongmi Luo ◽  
Weizhang Huang ◽  
Jianxian Qiu
Keyword(s):  
Kdv Type Equations

scholarly journals Breathers and the Dynamics of Solutions in KdV Type Equations

2018 ◽  
Vol 367 (2) ◽  
pp. 581-598 ◽  
Author(s):  
Claudio Muñoz ◽  
Gustavo Ponce
Keyword(s):  
Kdv Type Equations
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