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A large family of nonsingular rational solutions of the Kadomtsev-Petviashvili (KP) I equation are investigated. These solutions are constructed via the Gramian method and are identified as points in a complex Grassmannian. Each solution is a traveli
Externí odkaz:
http://arxiv.org/abs/2204.07872
A family of nonsingular rational solutions of the Kadomtsev-Petviashvili (KP) I equation are investigated. These solutions have multiple peaks whose heights are time-dependent and the peak trajectories in the $xy$-plane are altered after collision. T
Externí odkaz:
http://arxiv.org/abs/2111.05519
Publikováno v:
In Physica D: Nonlinear Phenomena April 2023 446
Autor:
Bihun, Oksana, Chakravarty, Sarbarish
Publikováno v:
SIGMA 13 (2017), 095, 24 pages
Dubrovin [Lecture Notes in Math., Vol. 1620, Springer, Berlin, 1996, 120-348] showed that the Chazy XII equation $y'''- 2yy''+3y'^2 = K(6y'-y^2)^2$, $K \in \mathbb{C}$, is equivalent to a projective-invariant equation for an affine connection on a on
Externí odkaz:
http://arxiv.org/abs/1712.09033
Publikováno v:
Phys. Lett. A Vol. 382, Iss. 7 (2018) 455-460
The equations for the general Darboux-Halphen system obtained as a reduction of the self-dual Yang-Mills can be transformed to a third-order system which resembles the classical Darboux-Halphen system with a common additive terms. It is shown that th
Externí odkaz:
http://arxiv.org/abs/1710.00158
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Autor:
Chakravarty, Sarbarish, Kodama, Yuji
We often observe that waves on the surface of shallow water form complex web-like patterns. They are examples of nonlinear waves, and these patterns are generated by nonlinear interactions among several obliquely propagating waves. In this note, we d
Externí odkaz:
http://arxiv.org/abs/1309.2689
Publikováno v:
Applicable Analysis, 89 (2010) 529-545
The line-soliton solutions of the Kadomtsev--Petviashvili (KP) equation are investigated in this article using the tau-function formalism. In particular, the Wronskian and the Grammian forms of the tau-function are discussed, and the equivalence of t
Externí odkaz:
http://arxiv.org/abs/0911.2290
The Chazy equation $y''' = 2yy'' - 3y'^2$ is derived from the automorphic properties of Schwarz triangle functions $S(\alpha, \beta, \gamma; z)$. It is shown that solutions $y$ which are analytic in the fundamental domain of these triangle functions,
Externí odkaz:
http://arxiv.org/abs/0902.3468
Autor:
Chakravarty, Sarbarish
Publikováno v:
Nonlinear Dynamics; Jan2024, Vol. 112 Issue 1, p575-589, 15p