Fractal Solitons, Arbitrary Function Solutions, Exact Periodic Wave and Breathers for a Nonlinear Partial Differential Equation by Using Bilinear Neural Network Method

Zhang, Runfa; Bilige, Sudao; Chaolu, Temuer

doi:10.1007/s11424-020-9392-5

Cited by 135 publications

(24 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Example 2. n solitons with periodic cnoidal background waves. 53,54 If one of w 1 and w 2 in Example 1 is replaced by a periodic solution, say,…”

Section: Special Linear Superpositions Of the Fifth-order Pbkp Equati...mentioning

confidence: 99%

“…Example n solitons with periodic cnoidal background waves 53,54 . If one of w 1 and w 2 in Example 1 is replaced by a periodic solution, say,

w_{2 x} = 2 k^{2} m^{2} {cn}^{2} ((), k x + false[4 k^{3} false(2 m^{2} - 1 false) - c k false] y + false[5 c^{2} k - 60 k^{3} false(2 m^{2} - 1 false) c + 72 k^{5} false(7 m^{4} - 7 m^{2} + 2 false) false] t + ξ_{0}, m),

where

cn false(ξ, m false)

is a Jacobi cn function with the modulus m ; then, w 7 = w 1 + w 2 becomes n solitons moving on a periodic cnoidal background wave.…”

Section: Special Linear Superpositions Of the Pbkp Hierarchymentioning

confidence: 99%

See 1 more Smart Citation

Decompositions and linear superpositions of B‐type Kadomtsev‐Petviashvili equations

Hao

Sen-Yue

2022

Math Methods in App Sciences

View full text Add to dashboard Cite

The existence of decomposition solutions of the well-known nonlinear BKP hierarchy is explored. It is shown that these decompositions provide simple and interesting relationships between classical integrable systems and the BKP hierarchy. Further, some special decomposition solutions display a rare property: they can be linearly superposed. With the emphasis on the case of the fifth BKP equation, the structure characteristic having linear superposition solutions is analyzed. Finally, we obtain similar superposed solutions in the dispersionless BKP hierarchy.

show abstract

“…Example 2. n solitons with periodic cnoidal background waves. 53,54 If one of w 1 and w 2 in Example 1 is replaced by a periodic solution, say,…”

Section: Special Linear Superpositions Of the Fifth-order Pbkp Equati...mentioning

confidence: 99%

“…Example n solitons with periodic cnoidal background waves 53,54 . If one of w 1 and w 2 in Example 1 is replaced by a periodic solution, say,

w_{2 x} = 2 k^{2} m^{2} {cn}^{2} ((), k x + false[4 k^{3} false(2 m^{2} - 1 false) - c k false] y + false[5 c^{2} k - 60 k^{3} false(2 m^{2} - 1 false) c + 72 k^{5} false(7 m^{4} - 7 m^{2} + 2 false) false] t + ξ_{0}, m),

where

cn false(ξ, m false)

is a Jacobi cn function with the modulus m ; then, w 7 = w 1 + w 2 becomes n solitons moving on a periodic cnoidal background wave.…”

Section: Special Linear Superpositions Of the Pbkp Hierarchymentioning

confidence: 99%

Decompositions and linear superpositions of B‐type Kadomtsev‐Petviashvili equations

Hao

Sen-Yue

2022

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…It is worth mentioning that the BNNM framework has been able to construct lump solutions, periodic solutions, bright-dark solitons solutions, and so on. [29][30][31][32][33][34] The deeper the framework of BNNM, the more diverse the test functions become, but this also causes a computational burden. Therefore, most of the current classical framework is based on one hidden layer to build test function.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Zhang and Bilige 28 combined the shallow neural network model with the bilinear method called bilinear neural network method (BNNM) to flexibly produce a variety of test functions, based on which more unknown and interesting solutions to NLEEs can be explored. It is worth mentioning that the BNNM framework has been able to construct lump solutions, periodic solutions, bright–dark solitons solutions, and so on 29–34 . The deeper the framework of BNNM, the more diverse the test functions become, but this also causes a computational burden.…”

Section: Introductionmentioning

confidence: 99%

Three types of periodic solutions of new (3 + 1)‐dimensional Boiti–Leon–Manna–Pempinelli equation via bilinear neural network method

Qiao

Zhang

Yue

et al. 2022

Math Methods in App Sciences

View full text Add to dashboard Cite

In the paper, we search for some analytical solutions for a new (3 + 1)-dimension Boiti-Leon-Manna-Pempinelli (BLMP) equation. Based on the Hirota bilinear method, bilinear neural network framework expands to more than one hidden layer to construct test functions. By using the symbolic computation software Maple, periodic-type I, II, and III solutions of the new (3 + 1)-dimension BLMP equation are obtained. Besides, the evolution and dynamical characteristics of these solutions derived via the appropriate real values are also exhibited.

show abstract

“…Zhang et al proposed bilinear neural network method in [33][34][35]. Through these methods, so many valuable and interesting results have sprung up.…”

Section: Introductionmentioning

confidence: 99%

Evolution Behaviour of Breathers and Lump-N-Solitons (N → ∞) for the (2+1)-Dimensional Benjamin-Bona-Mahony-Burgers Equation

2022

Preprint

View full text Add to dashboard Cite

Several types of exact solution of the (2+1)-dimensional Benjamin-Bona-Mahony-Burgers (BBMB) equation will be reported in this research. On the basis of bilinear neural network method (BNNM), some specifific activation functions are precisely taken into the single hidden layer neural nework model, different forms of breather wave solutions, lump solutions and novel hybrid solutions are proposed. By means of symbolic computation and making use of Mathematica software, exact breather wave solutions, lump solutions and lump-N-soliton solutions are constructed completely. The obtained results enrich the knowledge of BBMB equation in the current studies. Various fifigures are plotted to exhibit the interesting evolution characteristic of theses waves vividly. The proposed methods effffectively enable us to understand and investigate the nonlinear evolution equations in plasma physics, oceanography, optical fifibers and flfluid mechanics.

show abstract

Fractal Solitons, Arbitrary Function Solutions, Exact Periodic Wave and Breathers for a Nonlinear Partial Differential Equation by Using Bilinear Neural Network Method

Cited by 135 publications

References 37 publications

Decompositions and linear superpositions of B‐type Kadomtsev‐Petviashvili equations

Decompositions and linear superpositions of B‐type Kadomtsev‐Petviashvili equations

Three types of periodic solutions of new (3 + 1)‐dimensional Boiti–Leon–Manna–Pempinelli equation via bilinear neural network method

Evolution Behaviour of Breathers and Lump-N-Solitons (N → ∞) for the (2+1)-Dimensional Benjamin-Bona-Mahony-Burgers Equation

Contact Info

Product

Resources

About