Exploring lump soliton solutions and wave interactions using new Inverse (G′/G) -expansion approach: applications to the (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation

In this research article, we propose a novel approach called the new Inverse (G '/G)-Expansion Method to discover new exact soliton solutions for the (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain (HFSC) equation. By employing the proposed method, we successfully derive various set of new exact soliton solutions for the HFSC equation. These soliton solutions of the HFSC equation find valuable applications in various fields, including optical fiber communications, plasma physics, condensed matter physics, and nonlinear dynamics. To gain a visual understanding and illustrate the nature of the derived soliton solutions, we present 3-dimensional plots, contour plots, and 2-dimensional plots. Through these visualizations, we comprehensively observe and analyze various structures, including lump solitons, interactions of lumps with waves, periodic solitons, breather-type solitons, and solitary waves. To establish a connection between the depicted graphics and real-world phenomena, we incorporate images of transverse waves in a rope, waves on the ocean's surface, the oscillations within the ocean depths, and bubbly waves in the application section. These real-world examples help us to bridge the gap between theoretical soliton behavior and physical occurrences, providing a deeper insight into the significance and applicability of our findings. These results significantly enhance our understanding of the (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation, and also demonstrate the effectiveness of the novel Inverse (G '/G)-expansion method in extracting exact soliton solutions under specific constraint conditions.

Automated summary

In this research article, a new Inverse (G '/G)-Expansion Method is proposed to discover exact soliton solutions for the (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation. Various new soliton solutions for the equation are successfully derived using this method. These results have important applications in multiple fields and are presented through visualizations to demonstrate different characteristics of the soliton solutions.