The patterns of lump solutions for PT-symmetric (2+1)-dimensional nonlocal Mel’nikov equation
Year: 2026
Type: article
Abstract: This paper systematically investigates high-order lump solutions of the parity-time ( PT ) -symmetric (2+1)-dimensional nonlocal Mel’nikov equation and reveals their patterns at a fixed time. Using the Hirota’s bilinear method combined with the technique of Kadomtsev-Petviashvili hierarchy reduction and Schur polynomials, high-order lump solutions are derived in the form of Gram determinants. When the internal parameters a 2 m 1 + 1 and b 2 m 2 + 1 are large and satisfy the constraint | b 2 m 2 + 1 | 1 2 m 2 + 1 = O ( | a 2 m 1 + 1 | 2 2 m 1 + 1 ) , a three-layer concentric geometric structure is distinctly exhibited in the solutions. The outer and intermediate regions are governed by fundamental lumps forming distinct polygonal configurations, including triangular, pentagonal, heptagonal shapes etc., whose spatial distributions are determined by the nonzero roots of two Yablonskii-Vorob’ev hierarchies. Moreover, the inner region can generate low-order lump solution, which may be singular or regular depending on the choices of m 1 , m 2 , and other free parameters. Furthermore, numerical simulations are performed to validate the theoretical predictions, demonstrating a high degree of agreement between true patterns of lump solutions and analytical predictions. These findings provide new insights into the patterns of high-order lump solutions for the nonlocal integrable systems.
Source: Nuclear Physics B
Authors: Xin Zhang, Zhonglong Zhao, Wei Chen, Yindi Liu
Institution: North University of China
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Award: G6647390541
OpenAlex ID: W7214995179