The Cauchy problem for the generalized hyperbolic Novikov-Veselov equation via the Moutard symmetries

Abstract

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 $\Ai(ξ)$ which in turn serves as a solution to the ordinary differential equation $\frac{d^{2}z}{d{\xi }^2}=\xi z$. 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 $\frac{d^{n-1}z}{d{\xi }^{n-1}}=\xi z$.

13 pages, 2 figures, 36 references. arXiv admin note: substantial text overlap with arXiv:1509.06078

References in corpus (5)

• Phantom scalar dark energy as modified gravity: understanding the origin of the Big Rip singularity
• Absence of exponentially localized solitons for the Novikov--Veselov equation at negative energy
• Mach-Type Soliton in the Novikov-Veselov Equation
• Relation between hyperbolic Nizhnik-Novikov-Veselov equation and stationary Davey-Stewartson II equation
• Transverse instability of plane wave soliton solutions of the Novikov-Veselov equation

Cited by in corpus (1)

• On the Question of the Bäcklund Transformations and Jordan Generalizations of the Second Painlevé Equation