| Summary: | In this study, we explore the occurrence of a variety of dissipative soliton solutions in the complex Swift-Hohenberg equation (CSHE) at a specific value of system parameters and its stability. The CSHE is an amplitude-modulation equation that governs the evolution of pattern-forming systems with temporal dynamics that have a broad range of solutions. To investigate a wide variety of dissipative solitons in the CSHE, we apply a modified variational formulation into the CSHE and examine the issue using snaking solitons trial functions. We analyzed the behavior of soliton solutions by varying a higher order Kerr nonlinearity and linear loss. Our analysis demonstrates that due to the instability of Jacobian eigenvalues rise from Hopf bifurcation and Routh-Hurwitz criterion, both criteria address the fixed points of Euler-Lagrange equations of the CSHE is unstable. Thus, the fixed points of CSHE are unstable-stable focus, and exploding solitons occur in the system when the higher-order Kerr nonlinearity and linear loss are negative. © 2024 Author(s).
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