Browsing by Subject "Hirota method"

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    (2 + 1)-dimensional AKNS(−N) systems II
    (Elsevier BV, 2021-06) Gürses, Metin; Pekcan, Aslı
    In our previous work (Gürses and Pekcan, 2019, [40]) we started to investigate negative AKNS(−N) hierarchy in (2 + 1)-dimensions. We were able to obtain only the first three, N = 0, 1, 2, members of this hierarchy. The main difficulty was the nonexistence of the Hirota formulation of the AKNS(N) hierarchy for N ≥ 3. Here in this work we overcome this difficulty for N = 3, 4 and obtain Hirota bilinear forms of (2 + 1)-dimensional AKNS(−N) equations for these members. We study the local and nonlocal reductions of these systems of equations and obtain several new integrable local and nonlocal equations in (2 + 1)- dimensions. We also give one-, two-, and three-soliton solutions of the reduced equations
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    Multi-component AKNS systems
    (Elsevier, 2022-12-31) Gürses, Metin; Pekcan, A.
    We study two members of the multi-component AKNS hierarchy. These are multi-NLS and multi-MKdV systems. We derive the Hirota bilinear forms of these equations and obtain soliton solutions. We find all possible local and nonlocal reductions of these systems of equations and give a prescription to obtain their soliton solutions. We derive also -dimensional extensions of the multi-component AKNS systems.
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    Nonlocal KdV equations
    (Elsevier, 2020) Gürses, Metin; Pekcan, A.
    Writing the Hirota-Satsuma (HS) system of equations in a symmetrical form we find its local and new nonlocal reductions. It turns out that all reductions of the HS system are Korteweg-de Vries (KdV), complex KdV, and new nonlocal KdV equations. We obtain one-soliton solutions of these KdV equations by using the method of Hirota bilinearization.