Multiple soliton solutions for the new <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml45" display="inline" overflow="scroll" altimg="si45.gif"><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-dimensional Korteweg–de Vries equation by multiple exp-function method

Liu, Jian-Guo; Zhou, Li; He, Yan

doi:10.1016/j.aml.2018.01.010

Cited by 61 publications

(16 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The above results supplement the existing theories of rational, soliton and dromion-type solutions obtained earlier by using Hirota perturbation technique [15], symmetry reductions [4,10,34], symmetry constraints [3,11,12,49], multiple exp-function methods [13] and the Riemann-Hilbert technique [33].…”

Section: Diverse Lump and Interaction Solutionssupporting

confidence: 86%

Lump and Interaction Solutions of Linear PDEs in (3 + 1)-Dimensions

Ma¹

2019

EAJAM

View full text Add to dashboard Cite

show abstract

Section: Diverse Lump and Interaction Solutionssupporting

confidence: 86%

Lump and Interaction Solutions of Linear PDEs in (3 + 1)-Dimensions

Ma¹

2019

EAJAM

View full text Add to dashboard Cite

show abstract

“…The corresponding lump solution, defined by (17), for the special cgHSI equation 20 The results enrich the context of lumps and solitons, adding a new example of (2+1)-dimensional nonlinear equations which possess lump structures. An illustrative example of the resulting cgHSI equation and its lump solution were presented with Maple, together with three 3d-plots and contour plots of the lump solution.…”

Section: Yufeng Zhang Wen-xiu Ma and Jin-yun Yangmentioning

confidence: 90%

A study on lump solutions to a (2+1)-dimensional completely generalized Hirota-Satsuma-Ito equation

Zhang¹,

Ma²

2020

Discrete &Amp; Continuous Dynamical Systems - S

View full text Add to dashboard Cite

We aim to generalize the (2+1)-dimensional Hirota-Satsuma-Ito (HSI) equation, passing the three-soliton test, to a new one which still has diverse solution structures. We add all second-order derivative terms to the HSI equation but demand the existence of lump solutions. Such lump solutions are formulated in terms of the coefficients, except two, in the resulting generalized HSI equation. As an illustrative example, a special completely generalized HSI equation is given, together with a lump solution, and three 3d-plots and contour plots of the lump solution are made to elucidate the characteristics of the presented lump solutions.

show abstract

“…All the exact solutions generated above add valuable insights into the existing theories on soliton solutions and dromion-type solutions, developed through various powerful solution techniques including the Hirota perturbation approach, the Riemann-Hilbert approach, the Wronskian technique, symmetry reductions, and symmetry constraints (see, e.g., [21][22][23][24][25][26][27][28][29][30][31]).…”

Section: Lump Solutionsmentioning

confidence: 99%

A Study on Lump Solutions to a Generalized Hirota‐Satsuma‐Ito Equation in (2+1)‐Dimensions

Khalique

2018

Complexity

View full text Add to dashboard Cite

The Hirota-Satsuma-Ito equation in (2+1)-dimensions passes the three-soliton test. This paper aims to generalize this equation to a new one which still has abundant interesting solution structures. Based on the Hirota bilinear formulation, a symbolic computation with a new class of Hirota-Satsuma-Ito type equations involving general second-order derivative terms is conducted to require having lump solutions. Explicit expressions for lump solutions are successfully presented in terms of coefficients in a generalized Hirota-Satsuma-Ito equation. Three-dimensional plots and contour plots of a special presented lump solution are made to shed light on the characteristic of the resulting lump solutions.

show abstract

Multiple soliton solutions for the new (2+1)-dimensional Korteweg–de Vries equation by multiple exp-function method

Cited by 61 publications

References 32 publications

Lump and Interaction Solutions of Linear PDEs in (3 + 1)-Dimensions

Lump and Interaction Solutions of Linear PDEs in (3 + 1)-Dimensions

A study on lump solutions to a (2+1)-dimensional completely generalized Hirota-Satsuma-Ito equation

A Study on Lump Solutions to a Generalized Hirota‐Satsuma‐Ito Equation in (2+1)‐Dimensions

Contact Info

Product

Resources

About