Backlund Transformations for Liouville Equations with Exponential Nonlinearity

被引：2

作者：

Redkina, Tatyana V. ^{[1
,2
]}

Zakinyan, Robert G. ^{[2
,3
]}

Zakinyan, Arthur R. ^{[2
,3
]}

Novikova, Olga V. ^{[2
,4
]}

机构：

[1] North Caucasus Fed Univ, Fac Math & Comp Sci, 1 Pushkin St, Stavropol 355017, Russia

[2] North Caucasus Ctr Math Res, 1 Pushkin St, Stavropol 355017, Russia

[3] North Caucasus Fed Univ, Phys Tech Fac, 1 Pushkin St, Stavropol 355017, Russia

[4] North Caucasus Fed Univ, Inst Digital Dev, 2 Kulakov Ave, Stavropol 355017, Russia

来源：

AXIOMS | 2021年 / 10卷 / 04期

关键词：

nonlinear equations in partial derivatives; hyperbolic equations; Backlund transformations; Clairin's method; differential relationships; the Liouville equation; DIFFERENTIAL-EQUATIONS;

D O I：

10.3390/axioms10040337

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work aims to obtain new transformations and auto-Backlund transformations for generalized Liouville equations with exponential nonlinearity having a factor depending on the first derivatives. This paper discusses the construction of Backlund transformations for nonlinear partial second-order derivatives of the soliton type with logarithmic nonlinearity and hyperbolic linear parts. The construction of transformations is based on the method proposed by Clairin for second-order equations of the Monge-Ampere type. For the equations studied in the article, using the Backlund transformations, new equations are found, which make it possible to find solutions to the original nonlinear equations and reveal the internal connections between various integrable equations.

引用

页数：16

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