Abstract
In this paper, we use the Riemann–Hilbert (RH) approach to examine the integrable three-coupled Lakshmanan–Porsezian–Daniel (LPD) model, which describes the dynamics of alpha helical protein with the interspine coupling at the fourth-order dispersion term. Through the spectral analysis of Lax pair, we construct the higher-order matrix RH problem for the three-coupled LPD model, when the jump matrix of this particular RH problem is a $$4\times 4$$ unit matrix, the exact N-soliton solutions of the three-coupled LPD model can be exhibited. As special examples, we also investigate the nonlinear dynamical behaviors of the single-soliton, two-soliton, three-soliton and breather soliton solutions. Finally, an integrable generalized N-component LPD model with its linear spectral problem is discussed.
Highlights
Since the nonlinear evolution equations can be widely used to describe some of the physics physical phenomena, such as nonlinear optical, quantum mechanics, fluid physics, plasma physics, etc
With the development of soliton theory, a series of methods for solving nonlinear development equations are proposed, such as the inverse scattering method [1], the Hirota’s bilinear method [2], the Backlund transformation method [3], the Darboux transformation (DT) method [4] and others [5, 6, 7, 8]. Based on these available methods, we have obtained a series of solutions of nonlinear evolution equations, including compaton solution, peakon solution, periodic sharp wave solution, Lump solution, breather solution, bright soliton, dark soliton, rogue waves, etc
We aim to investigate the soliton solutions of three-coupled LPD model (1.2) via the RH approach, and discuss the dynamic behavior of the soliton solutions
Summary
Since the nonlinear evolution equations can be widely used to describe some of the physics physical phenomena, such as nonlinear optical, quantum mechanics, fluid physics, plasma physics, etc. With the development of soliton theory, a series of methods for solving nonlinear development equations are proposed, such as the inverse scattering method [1], the Hirota’s bilinear method [2], the Backlund transformation method [3], the Darboux transformation (DT) method [4] and others [5, 6, 7, 8] Based on these available methods, we have obtained a series of solutions of nonlinear evolution equations, including compaton solution, peakon solution, periodic sharp wave solution, Lump solution, breather solution, bright soliton, dark soliton, rogue waves, etc. These solutions can further help to understand natural phenomena and laws.
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