Dynamical Behaviors of Lumpoff and Rogue Wave Solutions for Nonlocal Gardner Equation

In this paper, we got a novel kind of rogue waves with the predictability of (2 + 1)-dimensional nonlocal Gardner equation with the aid of Maple according to the Hirota bilinear model. We first construct a general quadratic function to derive the general lump solution for the mentioned equation. At the same time, the lumpoff solutions are demonstrated with more free autocephalous parameters, in which the lump solution is localized in all directions in space. Moreover, when the lump solution is cut by twin-solitons, special rogue waves are also introduced. Based on the data available in the literature, the resulting soliton solutions are innovative, developed, distinctive, and significant and can be applied to more complex phenomena, and they are immensely active for nonlinear models of classical and fractional-order type. To examine the dynamic behavior of the waves, contour 3D and 2D plots of several obtained findings are sketched by assigning specific values to the parameters. Furthermore, we obtain new sufficient solutions containing cross-kink, periodic-kink, multi-waves, and solitary wave solutions. It is worth noting that the emerging time and place of the rogue waves depend on the moving path of the lump solution.

[1]  M. Bayram,et al.  Derivation of optical solitons of dimensionless Fokas-Lenells equation with perturbation term using Sardar sub-equation method , 2022, Optical and Quantum Electronics.

[2]  Xibo Yuan,et al.  Virtual Voltage Vector Based Model Predictive Control for a Nine-Phase Open-End Winding PMSM With a Common DC Bus , 2022, IEEE Transactions on Industrial Electronics.

[3]  B. Samali,et al.  Influence of seismic orientation on the statistical distribution of nonlinear seismic response of the stiffness-eccentric structure , 2022, Structures.

[4]  M. Bayram,et al.  Optical solitons with Kudryashov’s sextic power-law nonlinearity , 2022, Optik.

[5]  A. Yusuf,et al.  Some novel analytical solutions of a new extented (2+1)-dimensional Boussinesq equation using a novel method , 2022, Journal of Ocean Engineering and Science.

[6]  Huailei Cheng,et al.  Bridging the gap between laboratory and field moduli of asphalt layer for pavement design and assessment: A comprehensive loading frequency-based approach , 2022, Frontiers of Structural and Civil Engineering.

[7]  A. Akgül,et al.  Analytical study of soliton solutions for an improved perturbed Schrödinger equation with Kerr law non-linearity in non-linear optics by an expansion algorithm , 2021 .

[8]  H. Rezazadeh,et al.  Propagation of new dynamics of longitudinal bud equation among a magneto-electro-elastic round rod , 2021, Modern Physics Letters B.

[9]  Guoqing Zhou,et al.  An innovative echo detection system with STM32 gated and PMT adjustable gain for airborne LiDAR , 2021, International Journal of Remote Sensing.

[10]  M. Bayram,et al.  Optical solitons of the (2+1)-dimensional Biswas–Milovic equation using modified extended tanh-function method , 2021 .

[11]  Yuhong Wang,et al.  Effects of actual loading waveforms on the fatigue behaviours of asphalt mixtures , 2021 .

[12]  Ali Akgül,et al.  A Novel Homotopy Perturbation Method with Applications to Nonlinear Fractional Order KdV and Burger Equation with Exponential-Decay Kernel , 2021, Journal of Function Spaces.

[13]  Hijaz Ahmad,et al.  The fractional comparative study of the non-linear directional couplers in non-linear optics , 2021, Results in Physics.

[14]  Wei Zhang,et al.  Experimental study of predamaged columns strengthened by HPFL and BSP under combined load cases , 2021, Structure and Infrastructure Engineering.

[15]  M. Bayram,et al.  Soliton Solutions of $$(2+1)$$ Dimensional Heisenberg Ferromagnetic Spin Equation by the Extended Rational $$sine-cosine$$ and $$sinh-cosh$$ Method , 2021, International Journal of Applied and Computational Mathematics.

[16]  Muhammad Imran Asjad,et al.  The fractional analysis of fusion and fission process in plasma physics , 2021, Physica Scripta.

[17]  Jalil Manafian,et al.  .An optimal Galerkin-homotopy asymptotic method applied to the nonlinear second-order BVPs , 2021, Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan.

[18]  Ardashir Mohammadzadeh,et al.  A Novel Fractional-Order Multiple-Model Type-3 Fuzzy Control for Nonlinear Systems with Unmodeled Dynamics , 2021, International Journal of Fuzzy Systems.

[19]  Sector Beam Synthesis in Linear Antenna Arrays using Social Group Optimization Algorithm , 2021, National Journal of Antennas and Propagation.

[20]  Wei Zhang,et al.  Experimental study on circular steel tube-confined reinforced UHPC columns under axial loading , 2021 .

[21]  H. Rezazadeh,et al.  A study of travelling, periodic, quasiperiodic and chaotic structures of perturbed Fokas–Lenells model , 2021, Pramana.

[22]  Emrullah Yasar,et al.  Breather-type and multi-wave solutions for (2+1)-dimensional nonlocal Gardner equation , 2021, Appl. Math. Comput..

[23]  Kottakkaran Sooppy Nisar,et al.  Novel multiple soliton solutions for some nonlinear PDEs via multiple Exp-function method , 2021 .

[24]  Bang-Qing Li,et al.  Extended generalized Darboux transformation to hybrid rogue wave and breather solutions for a nonlinear Schrödinger equation , 2020, Appl. Math. Comput..

[25]  Hojat Karami,et al.  Combination of Group Method of Data Handling (GMDH) and Computational Fluid Dynamics (CFD) for Prediction of Velocity in Channel Intake , 2020 .

[26]  F. Aslanova.  A Comparative Study of the Hardness and Force Analysis Methods Used in Truss Optimization with Metaheuristic Algorithms and Under Dynamic Loading , 2020, Journal of Research in Science, Engineering and Technology.

[27]  Xue-Wei Yan,et al.  Lax pair, Darboux-dressing transformation and localized waves of the coupled mixed derivative nonlinear Schrödinger equation in a birefringent optical fiber , 2020, Appl. Math. Lett..

[28]  Yunqing Yang,et al.  Darboux–Bäcklund transformation, breather and rogue wave solutions for Ablowitz–Ladik equation , 2020 .

[29]  S. Pospíšil,et al.  Experimental Investigation on Rehabilitation of Corroded RC Columns with BSP and HPFL under Combined Loadings , 2020, Journal of Structural Engineering.

[30]  Onur Alp Ilhan,et al.  Periodic wave solutions and stability analysis for the KP-BBM equation with abundant novel interaction solutions , 2020, Physica Scripta.

[31]  Yajuan Tang,et al.  Deep Learning for Feynman's Path Integral in Strong-Field Time-Dependent Dynamics. , 2020, Physical review letters.

[32]  The Use of Deep Data Locality towards a Hadoop Performance Analysis Framework , 2020, International Journal of Communication and Computer Technologies.

[33]  J. Manafian,et al.  Breather wave, periodic, and cross‐kink solutions to the generalized Bogoyavlensky‐Konopelchenko equation , 2019, Mathematical Methods in the Applied Sciences.

[34]  M. Goyal,et al.  An efficient technique for a time fractional model of lassa hemorrhagic fever spreading in pregnant women , 2019, The European Physical Journal Plus.

[35]  Behnam Mohammadi-Ivatloo,et al.  Lump-type solutions and interaction phenomenon to the (2+1)-dimensional Breaking Soliton equation , 2019, Appl. Math. Comput..

[36]  J. T. Tenreiro Machado,et al.  A new fractal nonlinear Burgers' equation arising in the acoustic signals propagation , 2019, Mathematical Methods in the Applied Sciences.

[37]  H. M. Baskonus,et al.  Solitons in conformable time-fractional Wu–Zhang system arising in coastal design , 2019, Pramana.

[38]  H. M. Baskonus,et al.  Complex surfaces to the fractional (2 + 1)-dimensional Boussinesq dynamical model with the local M-derivative , 2019, The European Physical Journal Plus.

[39]  Mukesh Kumar,et al.  On Lie symmetries and invariant solutions of (2+1)-dimensional Gardner equation , 2019, Commun. Nonlinear Sci. Numer. Simul..

[40]  H. Bulut,et al.  Jacobi elliptic function solutions of the double dispersive equation in the Murnaghan's rod , 2019, The European Physical Journal Plus.

[41]  J. Manafian,et al.  Lump-type solutions and interaction phenomenon to the bidirectional Sawada–Kotera equation , 2019, Pramana.

[42]  Runfa Zhang,et al.  Abundant Lump Solutions and Interaction Phenomena to the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony Equation , 2018 .

[43]  T. Sulaiman,et al.  Bright, dark optical and other solitons to the generalized higher-order NLSE in optical fibers , 2018, Optical and Quantum Electronics.

[44]  X. Geng,et al.  N-Soliton Solution and Soliton Resonances for the (2+1)-Dimensional Inhomogeneous Gardner Equation* , 2017 .

[45]  Wen-Xiu Ma,et al.  Lump-type solutions to nonlinear differential equations derived from generalized bilinear equations , 2016 .

[46]  Jingyuan Yang,et al.  Lump solutions to the BKP equation by symbolic computation , 2016 .

[47]  Biao Li,et al.  Nonlocal symmetry and exact solutions of the (2+1)-dimensional Gardner equation , 2016 .

[48]  H. M. Baskonus,et al.  Exponential prototype structures for (2+1)-dimensional Boiti-Leon-Pempinelli systems in mathematical physics , 2016 .

[49]  Wenxiu Ma,et al.  Lump solutions to the Kadomtsev–Petviashvili equation , 2015 .

[50]  Bo Tian,et al.  Integrable decompositions for the (2+1)-dimensional Gardner equation , 2010 .

[51]  Abdul-Majid Wazwaz,et al.  New solitons and kink solutions for the Gardner equation , 2007 .

[52]  Xianguo Geng,et al.  N-soliton solution and its Wronskian form of a (3+1)-dimensional nonlinear evolution equation , 2007 .

[53]  H. Tam,et al.  On the (2+1)-dimensional Gardner equation: Determinant solutions and pfaffianization☆ , 2007 .

[54]  B. Konopelchenko.  Inverse spectral transform for the (2 + 1)-dimensional Gardner equation , 1991 .

[55]  C. S. Gardner,et al.  Korteweg‐de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion , 1968 .

[56]  F. Jarad,et al.  A hybrid analytical technique for solving nonlinear fractional order PDEs of power law kernel: Application to KdV and Fornberg-Witham equations , 2022, AIMS Mathematics.

[57]  Guoqing Zhou,et al.  Gaussian Inflection Point Selection for LiDAR Hidden Echo Signal Decomposition , 2022, IEEE Geoscience and Remote Sensing Letters.

[58]  Hong-Cai Ma,et al.  Solitons, Breathers, and Lump Solutions to the (2 + 1)-Dimensional Generalized Calogero-Bogoyavlenskii-Schiff Equation , 2021, Complex..

[59]  Guoqing Zhou,et al.  Comparison Analysis of Five Waveform Decomposition Algorithms for the Airborne LiDAR Echo Signal , 2021, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[60]  Yi-Peng Xu,et al.  Optimal structure design of a PV/FC HRES using amended Water Strider Algorithm , 2021 .

[61]  A. Oleinik,et al.  Calculation methodology for geometrical characteristics of the forming tool for rib cold rolling , 2020 .

[62]  R. Miura.  A derivation of Gardner’s equation , 1997 .