A unified concatenation model for plasma physics: Integrability and soliton solutions

In numerous fields of mathematical physics, including nuclear physics, fluid dynamics, quantum optics, and plasma physics, the idea of nonlinear evolution equation has left an enduring impression. The concept of concatenation model has recently gained its popularity after its first appearance during 2014. Such a model was proposed in nonlinear optics and exists in two forms: the concatenation model and the dispersive concatenation model, both of which depend on the fundamental components concatenated for their formulation. Likewise, the current paper proposes a concatenation model from plasma physics whose fundamental components are the Kaup-Newell equation, Chen-Lee-Liu equation and the Gerdjikov-Ivanov equation. These encompass various concepts such as Langmuir waves, Alfvén waves, and cold plasmas, which are commonly studied in plasma physics. The special cases of this newly structured concatenation model are apparent as discussed in detail in the subsequent section. Next, the model's integrability is examined. For this recently developed model, the soliton solutions are obtained using two integration techniques. The methods are the enhanced direct algebraic method and the modified sub-ODE (ordinary differential equation) approach. These two approaches use the intermediary Jacobi's and Weierstrass' elliptic functions, respectively, to obtain the soliton solutions. Solitons can be used to identify special cases of these functions. We utilize the parameter constraints that naturally arise from the two integration approaches. Following an introduction to the model, these are covered in detail in the remaining text. The concatenated DNLS model formulated here offers a single parameterized framework in which KN, CLL and GI arise as embedded limits; the tunable derivative couplings <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo> <mml:mrow><mml:msub><mml:mi>c</mml:mi> <mml:mn>1</mml:mn></mml:msub> <mml:mo>,</mml:mo> <mml:msub><mml:mi>c</mml:mi> <mml:mn>2</mml:mn></mml:msub> <mml:mo>,</mml:mo> <mml:msub><mml:mi>c</mml:mi> <mml:mn>3</mml:mn></mml:msub> </mml:mrow> <mml:mo>)</mml:mo></mml:mrow> </mml:math> and higher-order amplitudinal terms <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo> <mml:mrow><mml:msub><mml:mi>b</mml:mi> <mml:mn>1</mml:mn></mml:msub> <mml:mo>,</mml:mo> <mml:msub><mml:mi>b</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:mrow> <mml:mo>)</mml:mo></mml:mrow> </mml:math> enable controlled passage between convective self-steepening, mixed derivative nonlinearities and quintic saturation. This structure is novel in providing a unified description that consolidates previously separate DNLS-type models into a single tractable form, thereby enabling systematic exploration of plasma nonlinearities across distinct physical regimes.•The paper proposes a novel concatenation model in plasma physics constructed from three fundamental equations-the Kaup-Newell, Chen-Lee-Liu, and Gerdjikov-Ivanov equations-representing key plasma wave phenomena such as Langmuir and Alfvén waves.•Soliton solutions of the model are analytically derived using two powerful integration techniques: the enhanced direct algebraic method (involving Jacobi elliptic functions) and the modified sub-ODE method (utilizing Weierstrass elliptic functions).•The study identifies integrability conditions and parameter constraints from both solution approaches, offering insight into special cases of the model and contributing to the theoretical understanding of nonlinear plasma wave dynamics.