Novel soliton molecules and breather-positon on zero background for the complex modified KdV equation

Breather Positons and Rogue Waves for the Nonlocal Fokas-Lenells Equation

“…Can we find the trajectories of breather positons as in Ref. [17]? If this works, then we can make some important conclusions about the dynamics.…”

“…Since breather positons were proposed by Wang et al [10], it has been a difficult problem to study the change trend of breather positons over time. It is always a difficult problem to find the trajectories of breather positons [10,16,17]. Not to mention, let us study the dynamic properties of breather positons like decomposing smooth positons [7][8][9].…”

Partial-limit solutions and rational solutions with parameter for the Fokas-Lenells equation

“…In addition, mixed solutions can be obtained from a more general form of matrix A, e.g., a combined matrix A = Diag(A 1 , • • • , A s , J N −2s [a s+1 ]), where A j is defined in (32). Using formulae ( 5) and ( 14) one can get new solutions to the massive Thirring model (4) from our solutions to the FL equation.…”

“…The amplitudes of the waves are not constants but slowly changing and finally they approach to Note that in the rational solution the two waves asymptotically travel along parabolas, which is different from the asymptotic tracks of double-pole solutions of solitons which usually governed by logarithmic functions (cf. [22,27,31,32].…”

Construction of higher-order smooth positons and breather positons via Hirota’s bilinear method

“…In fact, there have been some mature schemes for constructing breather positons via degenerate Darboux transformation: Starting from the plane wave solution, breather positons with a nonzero background will be derived when the spectral parameters λ 2 j−1 tend to a specific value λ 1 [15]; Based on degenerate Darboux transformation with a zero seed solution, Ref. [18] describes another mechanism for generating breather positons with a zero background using module resonance conditions.…”