物理学报2026，Vol.75Issue(12)：1-11,11.DOI:10.7498/aps.75.20251591
高阶矩阵非线性薛定谔方程中孤子相互作用与束缚态调控
Control of solitonic interactions and bound-states in the higher-order matrix nonlinear Schrödinger equation
摘要
Abstract
We investigate the control of solitonic interactions and bound-state formations in the higher-order matrix nonlinear Schrödinger equation with the sign-alternating nonlinearity and third-order dispersion.By employing the binary Darboux transformation,we construct explicit N-soliton solutions from a zero seed background.Adjusting these parameters ljk(j,k=1,2,3,4)enables systematic generation of various bound-state soliton structures. For the second-order case(N=2),we obtain several distinct configurations depending on the relations between the matrices C1 and C2(constructed from ljk)and their determinants.When C1≠C2 with det(C2)=idet(C1)and det(C1C2)=-i,the components q1 and q2 exhibit breathing solitons.Varying the spectral parameters λj transforms them into parallel breathing solitons with different amplitudes.For C1 ≠ C2 with det(C2)=idet(C1)and det(C1C2)=i,the components become linearly independent,yielding a bound state of one ordinary soliton and one breathing soliton.When C1=C2 with det(C1C2)=-1,the solitons propagate with identical amplitude and velocity while displaying periodic attraction and repulsion,which is a typical soliton molecule behavior accompanied by energy redistribution at the collision points.For C1=C2 with det(C1C2)=5/4-3i,we find the double-peaked bound-state solitons in q1 and single-peaked intertwined structures in q2. In the third-order case(N=3),we explore seven parameter regimes leading to even more complex composite states.These include:one soliton coexisting with two breathing solitons(the elastic interaction with constant velocity),one soliton with two ordinary solitons exhibiting phase shifts after the collision,one soliton with two double-peaked solitons where the amplitude changes indicate energy redistribution,and one soliton with two separated double-peaked solitons where both shape and separation are modified by energy exchange.In all cases,the binary Darboux transformation ensures that the solutions are exact and exhibit either elastic or inelastic interactions characterized by phase shifts,amplitude modulation,and periodic energy transfer among components. To verify the robustness of the obtained solutions,we perform numerical stability tests by adding 10％Gaussian noise to the analytical profile of the breathing soliton at different propagation distances.The shape fidelity remains high,confirming the physical reliability of these structures under small perturbations. The results provide a theoretical foundation for manipulating multi-component soliton states in conservative nonlinear systems and offer insights into the design of all optical logic devices or soliton-based communication links where controlled interactions are essential.关键词
高阶矩阵非线性薛定谔方程/二元Darboux变换/孤子相互作用/束缚态孤子Key words
higher-order matrix nonlinear Schrödinger equation/binary Darboux transformation/solitonic interactions/bound-state solitons引用本文复制引用
曾平安,刘露,曾平平..高阶矩阵非线性薛定谔方程中孤子相互作用与束缚态调控[J].物理学报,2026,75(12):1-11,11.基金项目
国家自然科学基金(批准号:72272089,71902105)资助的课题. Project supported by the National Natural Science Foundation of China(Grant Nos.72272089,71902105). （批准号:72272089,71902105）
