论文标题
两部分长波 - 波浪共振模型中的一般高阶呼吸器和流氓波
General higher-order breathers and rogue waves in the two-component long-wave--short-wave resonance-interaction model
论文作者
论文摘要
两组分长波谐振相互作用（2-LSRI）模型的一般高阶呼吸器和流氓波（RW）溶液是通过双线性Kadomtsev-PetviaShvili层次层次结构方法得出的，并以确定性的方式给出。在特定的参数条件下，呼吸溶液可以减少到同质轨道轨道，或呼吸器和同型轨道的混合物。 RW解决方案的三个家族对应于简单的根，两个简单的根，以及与降低过程相关的代数方程的双根。 RW解决方案的第一家族由$ \ frac {n（n+1）} {2} $有限的基本RWS组成，第二个家庭由$ \ frac {n_1（n_1+1）} {2} {2} $ bounded buttared undarted rws与另一个$ \ frac undental undectional undementials $ \ frac} $ \ frac {n_2（n _2+1）在不同的有限状态（$ n，n_1，n_2 $为正整数）中，而第三个则具有$ {[\ wideHat {n} _1^2+\ wideHat {n} _2^2- _2^2- \ wideHat {n} _1（n} _1） （$ \ wideHat {n} _1，\ wideHat {n} _2 $是非阴性整数）。第二个家庭可以被视为第一家族的叠加，而第三个家庭可以是在特定参数选择下的堕落案例。这些不同的RW模式以图形方式说明。
General higher-order breather and rogue wave (RW) solutions to the two-component long wave--short wave resonance interaction (2-LSRI) model are derived via the bilinear Kadomtsev-Petviashvili hierarchy reduction method and are given in terms of determinants. Under particular parametric conditions, the breather solutions can reduce to homoclinic orbits, or a mixture of breathers and homoclinic orbits. There are three families of RW solutions, which correspond to a simple root, two simple roots, and a double root of an algebraic equation related to the dimension reduction procedure. The first family of RW solutions consists of $\frac{N(N+1)}{2}$ bounded fundamental RWs, the second family is composed of $\frac{N_1(N_1+1)}{2}$ bounded fundamental RWs coexisting with another $\frac{N_2(N_2+1)}{2}$ fundamental RWs of different bounded state ($N,N_1,N_2$ being positive integers), while the third one have ${[\widehat{N}_1^2+\widehat{N}_2^2-\widehat{N}_1(\widehat{N}_2-1)]}$ fundamental bounded RWs ($\widehat{N}_1,\widehat{N}_2$ being non-negative integers). The second family can be regarded as the superpositions of the first family, while the third family can be the degenerate case of the first family under particular parameter choices. These diverse RW patterns are illustrated graphically.
