The Cauchy Problem for the Generalized Hyperbolic Novikov-Veselov Equation via the Moutard Symmetries

被引：2

作者：

Yurova, Alla A. ^{[1
,2
]}

Yurov, Artyom, V ^{[1
]}

Yurov, Valerian A. ^{[1
]}

机构：

[1] Immanuel Kant Baltic Fed Univ, Dept Phys Math & Informat Technol, Al Nevsky St 14, Kaliningrad 236041, Russia

[2] Kaliningrad State Tech Univ, Math Dept, Sovetsky Ave 1, Kaliningrad 236000, Russia

来源：

SYMMETRY-BASEL | 2020年 / 12卷 / 12期

关键词：

Novikov-Veselov equation; Lax pair; Moutard symmetry; Cauchy problem; INVERSE SCATTERING; SOLITONS;

D O I：

10.3390/sym12122113

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We begin by introducing a new procedure for construction of the exact solutions to Cauchy problem of the real-valued (hyperbolic) Novikov-Veselov equation which is based on the Moutard symmetry. The procedure shown therein utilizes the well-known Airy function Ai(xi) which in turn serves as a solution to the ordinary differential equation d(2)z/d xi(2)=xi z. In the second part of the article we show that the aforementioned procedure can also work for the n-th order generalizations of the Novikov-Veselov equation, provided that one replaces the Airy function with the appropriate solution of the ordinary differential equation d(n-1)z/d xi(n-1)=xi z.

引用

页码：1 / 17

页数：17

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