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

Search citation statements

Order By: Relevance

Paper Sections

Select...

Nonlocal Conservation Laws2

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2016

2019

Publication Types

Select...

Article3

Book1

Relationship

Self Cite1

Independent3

Authors

Journals

Cited by 4 publications

(2 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

See 1 more Smart Citation

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.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…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%