Families of Rational and Semirational Solutions of the Partial Reverse Space-Time Nonlocal Mel′nikov Equation

Complexity 2020:1-18 (2020)

Abstract
Exact periodic and localized solutions of a nonlocal Mel′nikov equation are derived by the Hirota bilinear method. Many conventional nonlocal operators involve integration over a spatial or temporal domain. However, the present class of nonlocal equations depends on properties at selected far field points which result in a potential satisfying parity time symmetry. The present system of nonlocal partial differential equations consists of two dependent variables in two spatial dimensions and time, where the dependent variables physically represent a wave packet and an auxiliary scalar field. The periodic solutions may take the forms of breathers and line solitons. The localized solutions can include propagating lumps and rogue waves. These nonsingular solutions are obtained by appropriate choice of parameters in the Hirota expansion. Doubly periodic solutions are also computed with elliptic and theta functions. In sharp contrast with the local Mel′nikov equation, the auxiliary scalar field in the present set of solutions can attain complex values. Through a coordinate transformation, the governing equation can reduce to the Schrödinger–Boussinesq system.
Keywords No keywords specified (fix it)
Categories No categories specified
(categorize this paper)
DOI 10.1155/2020/2642654
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 49,128
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Sinusoidal Solutions to the Aesthetic Field Equations.M. Muraskin - 1980 - Foundations of Physics 10 (3-4):237-242.
Hidden Variables with Nonlocal Time.Hrvoje Nikolić - 2012 - Foundations of Physics 42 (5):632-646.

Analytics

Added to PP index
2020-05-23

Total views
1 ( #1,404,102 of 2,311,514 )

Recent downloads (6 months)
1 ( #753,566 of 2,311,514 )

How can I increase my downloads?

Downloads

Sorry, there are not enough data points to plot this chart.

My notes

Sign in to use this feature