Integrability of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>S</mml:mi></mml:math>-deformable surfaces: Conservation laws, Hamiltonian structures and more

Krasil’shchik, I.; Sergyeyev, Artur

doi:10.1016/j.geomphys.2015.07.016

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Nonlocal Conservation Laws2

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Cited by 4 publications

(2 citation statements)

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“…From equations (20) it also immediately follows that under the assumptions of Lemma 1 the covering τ ω is irreducible. Now return to the ABC equation (1).…”

Section: Nonlocal Conservation Lawsmentioning

confidence: 85%

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Infinitely many nonlocal conservation laws for the ABC equation with $$A+B+C\ne 0$$ A + B + C ≠ 0

Krasil’shchik

Sergyeyev

Morozov³

2016

Calc. Var.

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We construct an infinite hierarchy of nonlocal conservation laws for the ABC equation Au t u xy + Bu x u ty + Cu y u tx = 0, where A, B, C are nonzero constants and A + B + C = 0, using a nonisospectral Lax pair. As a byproduct, we present new coverings for the equation in question. The method of proof of nontriviality of the conservation laws under study is quite general and can be applied to many other integrable multidimensional systems.

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“…From equations (20) it also immediately follows that under the assumptions of Lemma 1 the covering τ ω is irreducible. Now return to the ABC equation (1).…”

Section: Nonlocal Conservation Lawsmentioning

confidence: 85%

“…e.g. [2,3,20,35] and references therein, an infinite sequence of (in general nonlocal) two-component conservation laws for (2) of the form…”

Section: Nonlocal Conservation Lawsmentioning

confidence: 99%