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1. Full Text New optical soliton solutions for nonlinear complex fractional Schrödinger equation via new auxiliary equation method and novel $$({G'}/{G})$$ (G′/G) -expansion method
by Khater, Mostafa M A and Seadawy, Aly R and Lu, Dianchen
Pramana, ISSN 0304-4289, 5/2018, Volume 90, Issue 5, pp. 1 - 20
In this research, we apply two different techniques on nonlinear complex fractional nonlinear Schrödinger equation which is a very important model in... 
new auxiliary equation method | optical solitary travelling wave solutions | Astrophysics and Astroparticles | novel $$\left( {G'}/{G}\right) $$ G ′ / G -expansion method | kink and antikink | Physics, general | Nonlinear complex fractional Schrödinger equation | Physics | Astronomy, Observations and Techniques | novel (G | G) -expansion method | BOUSSINESQ EQUATION | PHYSICS, MULTIDISCIPLINARY | BIFURCATIONS | novel (G '/G)-expansion method | FIBERS | TRAVELING-WAVE SOLUTIONS | EVOLUTION | Nonlinear complex fractional Schrodinger equation | GINZBURG-LANDAU EQUATION | BRIGHT | Quantum theory | Methods
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2. Full Text Bistable Bright-Dark solitary wave solutions of the (3+1)-dimensional Breaking soliton, Boussinesq equation with dual dispersion and modified Korteweg–de Vries–Kadomtsev–Petviashvili equations and their applications
by Tariq, Kalim Ul-Haq and Seadawy, A.R
Results in Physics, ISSN 2211-3797, 2017, Volume 7, pp. 1143 - 1149
The Boussinesq equation with dual dispersion and modified Korteweg–de Vries–Kadomtsev–Petviashvili equations describe weakly dispersive and small amplitude... 
Modified Korteweg–de Vries–Kadomtsev–Petviashvili equation | Breaking soliton equation | Boussinesq equation
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3. Full Text The ( G ′ G )-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics
by Wang, Mingliang and Li, Xiangzheng and Zhang, Jinliang
Physics Letters A, ISSN 0375-9601, 2008, Volume 372, Issue 4, pp. 417 - 423
The ( )-expansion method is firstly proposed, where satisfies a second order linear ordinary differential equation (LODE for short), by which the travelling... 
Travelling wave solutions | Hirota–Satsuma equations | KdV equation | Variant Boussinesq equations | ( [formula omitted])-expansion method | Homogeneous balance | Solitary wave solutions | mKdV equation | Hirota-Satsuma equations | G))-expansion method | frac(G | EXPANSION METHOD | F-EXPANSION | NONCOMPACT STRUCTURES | VARIANTS | PHYSICS, MULTIDISCIPLINARY | SCHRODINGER-EQUATION | SUB-ODE METHOD | (G '/G)-expansion method | PARTIAL-DIFFERENTIAL-EQUATIONS | solitary wave solutions | homogeneous balance | travelling wave solutions | variant Boussinesq equations | EXPLICIT
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4. Full Text Dynamical analysis of lump solutions for (3 + 1) dimensional generalized KP-Boussinesq equation and Its dimensionally reduced equations
by Kaur, Lakhveer and Wazwaz, Abdul-Majid
Physica Scripta, ISSN 0031-8949, 06/2018, Volume 93, Issue 7, p. 75203
This paper analyzes a new form of the (3+1) dimensional generalized Kadomtsev-Petviashvili (KP)-Boussinesq equation for exploring lump solutions by making use... 
Bilinear equations | Lump solutions | Dimensionally reduced new form of (3 + 1) dimensional generalized KP-Boussinesq equation | New form of (3 + 1) dimensional generalized KP-Boussinesq equation | SOLITON-SOLUTIONS | I EQUATION | SYMMETRY | RESONANCE | PHYSICS, MULTIDISCIPLINARY | Dimensionally reduced new form of (3+1) dimensional generalized KP-Boussinesq equation | COEFFICIENTS | New form of (3+1) dimensional generalized KP-Boussinesq equation
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5. Full Text Modified method of simplest equation for obtaining exact solutions of the Zakharov–Kuznetsov equation, the modified Zakharov–Kuznetsov equation, and their generalized forms
by Yu, Jianping and Wang, Deng-Shan and Sun, Yongli and Wu, Suping
Nonlinear Dynamics, ISSN 0924-090X, 9/2016, Volume 85, Issue 4, pp. 2449 - 2465
In this paper, we study the application of a version of the method of simplest equation for obtaining exact traveling wave solutions of the Zakharov–Kuznetsov... 
Engineering | Vibration, Dynamical Systems, Control | Modified Zakharov–Kuznetsov equation | Modified method of simplest equation | Exact solutions | Mechanics | Automotive Engineering | Zakharov–Kuznetsov equation | Mechanical Engineering | Zakharov-Kuznetsov equation | 1-SOLITON SOLUTION | DE-VRIES EQUATION | ENGINEERING, MECHANICAL | TRAVELING-WAVE SOLUTIONS | MECHANICS | PARTIAL-DIFFERENTIAL-EQUATIONS | SYMBOLIC COMPUTATION | TIME-DEPENDENT COEFFICIENTS | BOUSSINESQ EQUATIONS | Modified Zakharov-Kuznetsov equation | KDV EQUATION | NONLINEAR EVOLUTION-EQUATIONS | VARIABLE SEPARATION APPROACH | Information science | Methods | Traveling waves | Nonlinear equations | Partial differential equations | Mathematical analysis | Nonlinear differential equations
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6. Full Text Conservation laws, soliton solutions for modified Camassa–Holm equation and (2 + 1)-dimensional ZK–BBM equation
by Elboree, Mohammed K
Nonlinear Dynamics, ISSN 0924-090X, 9/2017, Volume 89, Issue 4, pp. 2979 - 2994
By using the multiplier approach, we construct the conservation laws and the corresponding conserved quantities for the modified Camassa–Holm equation and... 
Engineering | Vibration, Dynamical Systems, Control | Classical Mechanics | Multiplier | Automotive Engineering | Camassa–Holm equation | Mechanical Engineering | Soliton solutions | Zakharov–Kuznetsov–Benjamin–Bona–Mahoney equation | Semi-inverse variational principle | TRAVELING-WAVE SOLUTIONS | MECHANICS | PARTIAL-DIFFERENTIAL-EQUATIONS | Zakharov-Kuznetsov-Benjamin-Bona-Mahoney equation | BOUSSINESQ EQUATIONS | SYSTEMS | EVOLUTION-EQUATIONS | Camassa-Holm equation | ENGINEERING, MECHANICAL | Environmental law | Conservation laws | Solitary waves
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7. Full Text Rogue Waves for the Coupled Schrödinger--Boussinesq Equation and the Coupled Higgs Equation
by Mu, Gui and Qin, Zhenyun
J Phys Soc Jpn, ISSN 0031-9015, 8/2012, Volume 81, Issue 8, pp. 084001 - 084001-6
In this work, firstly it is shown that the coupled Schrödinger--Boussinesq equation, which governs the nonlinear propagation of coupled Langmuir and... 
Coupled higgs equation | Schrödinger-Boussinesq equation | Hirota technique | Rogue wave | Schrodinger-Boussinesq equation | PEREGRINE SOLITON | coupled Higgs equation | PLASMA | MODULATION INSTABILITY | PHYSICS, MULTIDISCIPLINARY | SURFACE | FREAK WAVES | ZAKHAROV EQUATIONS
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8. Full Text Application of the ( G ′ G )-expansion method for the Zhiber–Shabat equation and other related equations
by Borhanifar, A and Moghanlu, Ali Zamiri
Mathematical and Computer Modelling, ISSN 0895-7177, 2011, Volume 54, Issue 9, pp. 2109 - 2116
In this paper, the exact traveling wave solutions of the Zhiber–Shabat equation and the related equations: Liouville equation, Dodd–Bullough–Mikhailov (DBM)... 
Tzitzeica–Dodd–Bullough (TDB) equation | ( [formula omitted])-expansion method | Zhiber–Shabat equation | Dodd–Bullough–Mikhailov (DBM) equation | Traveling wave solutions | Liouville equation | Tzitzeica-Dodd-Bullough (TDB) equation | Dodd-Bullough-Mikhailov (DBM) equation | Zhiber-Shabat equation | (G'G)-expansion method | MATHEMATICAL PHYSICS | MATHEMATICS, APPLIED | SINE-GORDON EQUATION | EXTENDED TANH METHOD | (G '/G)-expansion method | TRAVELING-WAVE SOLUTIONS | EXP-FUNCTION METHOD | BOUSSINESQ EQUATIONS | NONLINEAR EVOLUTION-EQUATIONS
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9. Full Text Application of the ( G ′ G ) -expansion method for nonlinear evolution equations
by Bekir, Ahmet
Physics Letters A, ISSN 0375-9601, 2008, Volume 372, Issue 19, pp. 3400 - 3406
In this work, we established abundant travelling wave solutions for some nonlinear evolution equations. This method was used to construct travelling wave... 
Modified Zakharov–Kuznetsov equation | Konopelchenko–Dubrovsky equation | [formula omitted]-expansion method | Boussinesq equation | Konopelchenko-Dubrovsky equation | Modified Zakharov-Kuznetsov equation | G))-expansion method | frac(G | modified zakharov-kuznetsov equation | (G'/G)-expansion method | TRAVELING-WAVE SOLUTIONS | PHYSICS, MULTIDISCIPLINARY | EXP-FUNCTION METHOD | boussinesq equation | EXTENDED TANH METHOD | konopelchenko-dubrovsky equation
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10. Full Text Bäcklund transformation, rogue wave solutions and interaction phenomena for a (3+1) -dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation
by Yan, Xue-Wei and Tian, Shou-Fu and Dong, Min-Jie and Zou, Li
Nonlinear Dynamics, ISSN 0924-090X, 04/2018, Volume 92, Issue 2, pp. 709 - 720
Under investigation in this paper is the -dimensional B-type Kadomtsev-Petviashvili-Boussinesq (BKP-Boussinesq) equation, which can display the nonlinear... 
Interaction phenomena | Rogue waves | Bäcklund transformation | Traveling waves | Kink solitary waves | Bell’s polynomial | BKP–Boussinesq equation | BREATHER WAVES | INTEGRABILITY | FLUID-DYNAMICS | BKP-Boussinesq equation | INFINITE CONSERVATION-LAWS | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | ENGINEERING, MECHANICAL | QUASI-PERIODIC WAVES | MECHANICS | Bell's polynomial | SOLITARY WAVES | (2+1)-DIMENSIONAL ITO EQUATION | Backlund transformation | RATIONAL CHARACTERISTICS | Water waves | Mineral industry | Mining industry | Nonlinear dynamics | Nonlinear equations | Boussinesq equations | Transformations (mathematics) | Nonlinear evolution equations | Polynomials | Identities | Solitary waves | Breathers
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11. Full Text Application of the extended simplest equation method to the coupled Schrödinger–Boussinesq equation
by Bilige, Sudao and Chaolu, Temuer and Wang, Xiaomin
Applied Mathematics and Computation, ISSN 0096-3003, 11/2013, Volume 224, pp. 517 - 523
In this paper, we successfully construct the new exact traveling wave solutions of the coupled Schrödinger–Boussinesq equation by using the extended simplest... 
The coupled Schrödinger–Boussinesq equation | The extended simplest equation method | The traveling wave solutions | The coupled Schrödinger-Boussinesq equation | SYSTEM | NONLINEAR DIFFERENTIAL-EQUATIONS | MATHEMATICS, APPLIED | TRAVELING-WAVE SOLUTIONS | EXPANSION | KDV EQUATION | EVOLUTION-EQUATIONS | The coupled Schrodinger-Boussinesq equation | PLASMAS
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12. Nonlinear evolution equations and Painlevé test
by Steeb, W.-H and Euler, N
1988, ISBN 9789971507442, ix, 333
Differential equations, Nonlinear | Painlevé equations
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13. Full Text A further improved extended Fan sub-equation method and its application to the ( 3 + 1 )-dimensional Kadomstev–Petviashvili equation
by Zhang, Sheng and Xia, TieCheng
Physics Letters A, ISSN 0375-9601, 2006, Volume 356, Issue 2, pp. 119 - 123
A further improved extended Fan sub-equation method is proposed to seek more types of exact solutions of non-linear partial differential equations. Applying... 
Triangular-like solutions | Weierstrass elliptic doubly-like periodic solutions | The modified extended Fan sub-equation method | Jacobi elliptic wave function-like solutions | Soliton-like solutions | EXPANSION METHOD | SERIES | PHYSICS, MULTIDISCIPLINARY | soliton-like solutions | KDV-BURGERS EQUATION | VARIANT BOUSSINESQ EQUATIONS | TRAVELING-WAVE SOLUTIONS | MKDV | PARTIAL-DIFFERENTIAL-EQUATIONS | triangular-like solutions | COEFFICIENTS | the modified extended Fan sub-equation method
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14. Full Text Depth‐averaged non‐hydrostatic extension for shallow water equations with quadratic vertical pressure profile: equivalence to Boussinesq‐type equations
by Jeschke, Anja and Pedersen, Geir K and Vater, Stefan and Behrens, Jörn
International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 08/2017, Volume 84, Issue 10, pp. 569 - 583
Summary We reformulate the depth‐averaged non‐hydrostatic extension for shallow water equations to show equivalence with well‐known Boussinesq‐type equations.... 
pressure profile | free surface | Serre equations | non‐hydrostatic pressure | Green–Nagdhi equations | Boussinesq‐type equations | shallow water | non-hydrostatic pressure | Boussinesq-type equations | PHYSICS, FLUIDS & PLASMAS | ALGORITHM | SIMULATION | Green-Nagdhi equations | WAVE PROCESSES | FREE-SURFACE FLOW | FINITE-ELEMENT MODEL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Shallow water equations | Vertical profiles | Boussinesq equations | Asymptotic properties | Derivatives | Shallow water | Water depth | Pressure | Dispersion | Depth | Equations | Equivalence | Simulation | Mathematical analysis | Hydrostatic pressure | Spacetime | Boussinesq approximation | Scalars | Mathematical models | Case depth
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15. Full Text Further improved extended Fan sub-equation method and new exact solutions of the (2 + 1)-dimensional Broer–Kaup–Kupershmidt equations
by Zhang, Sheng and Xia, TieCheng
Applied Mathematics and Computation, ISSN 0096-3003, 2006, Volume 182, Issue 2, pp. 1651 - 1660
In this paper, a further improved extended Fan sub-equation method is proposed by taking a more general transformation to seek more types of exact solutions of... 
Triangular-like solutions | Weierstrass elliptic doubly-like periodic solutions | The modified extended Fan sub-equation method | Jacobi elliptic wave function-like solutions | Soliton-like solutions | VARIATIONAL-PRINCIPLES | MATHEMATICS, APPLIED | F-EXPANSION | ELLIPTIC FUNCTION EXPANSION | soliton-like solutions | HOMOTOPY PERTURBATION METHOD | KDV-BURGERS EQUATION | PERIODIC-WAVE SOLUTIONS | VARIANT BOUSSINESQ EQUATIONS | PARTIAL-DIFFERENTIAL-EQUATIONS | triangular-like solutions | NONLINEAR EVOLUTION-EQUATIONS | TANH-FUNCTION METHOD | the modified extended Fan sub-equation method
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16. Full Text Exact solutions of nonlinear conformable time-fractional Boussinesq equations using the exp (- ϕ(ε)) -expansion method
by Hosseini, K and Bekir, A and Ansari, R
Optical and Quantum Electronics, ISSN 0306-8919, 04/2017, Volume 49, Issue 4, p. 1
Nonlinear fractional Boussinesq equations are considered as an important class of fractional differential equations in mathematical physics. In this article, a... 
Nonlinear Boussinesq equations | Conformable time-fractional derivative | Hyperbolic, trigonometric and rational function solutions | Exp (- ϕ(ε)) -expansion method | QUANTUM SCIENCE & TECHNOLOGY | DIFFERENTIAL-EQUATIONS | FUNCTIONAL VARIABLE METHOD | EVOLUTION-EQUATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | SOLITON-SOLUTIONS | 1ST INTEGRAL METHOD | Exp(-phi/(epsilon))-expansion method | KUDRYASHOV METHOD | OPTICS | Mechanical engineering | Methods | Differential equations
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17. Full Text New interaction solutions from residual symmetry reduction and consistent Riccati expansion of the (2 $$\varvec{+}$$ + 1)-dimensional Boussinesq equation
by Liu, Xi-zhong and Yu, Jun and Lou, Zhi-Mei
Nonlinear Dynamics, ISSN 0924-090X, 6/2018, Volume 92, Issue 4, pp. 1469 - 1479
In this paper, the (2 $$+$$ + 1)-dimensional Boussinesq equation is studied by applying residual symmetry reduction method and consistent Riccati expansion... 
Residual symmetry | Engineering | Vibration, Dynamical Systems, Control | (2 $$+$$ + 1)-dimensional Boussinesq equation | Consistent Riccati expansion | Classical Mechanics | Automotive Engineering | Mechanical Engineering | (2 + 1)-dimensional Boussinesq equation | MECHANICS | (2+1)-dimensional Boussinesq equation | NONLOCAL SYMMETRIES | DARBOUX TRANSFORMATIONS | ENGINEERING, MECHANICAL | SOLITON | Reduction | Boussinesq equations | Interaction models | Dependent variables | Cnoidal waves | Transformations | Solitary waves | Symmetry
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18. Full Text General high-order breathers, lumps in the (2 + 1) -dimensional Boussinesq equation
by Liu, Yunkai and Li, Biao and An, Hong-Li
Nonlinear Dynamics, ISSN 0924-090X, 06/2018, Volume 92, Issue 4, pp. 2061 - 2076
Under investigation in this work is a generalized (2+1)-dimensional Boussinesq equation. By employing the Bell's polynomials, bilinear formalism of this... 
Bilinear transform method | Lump | (2+1)-Dimensional Boussinesq equation | Breather | WATER-WAVES | SOLITARY WAVE | MECHANICS | SOLITONS | DYNAMICS | ENGINEERING, MECHANICAL | ROGUE WAVES | Polynomials | Boussinesq equations | Perturbation | Formalism | Breathers
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19. Full Text Solving the (3+ 1) -dimensional KP–Boussinesq and BKP–Boussinesq equations by the simplified Hirota’s method
by Wazwaz, Abdul-Majid and El-Tantawy, S.A
Nonlinear Dynamics, ISSN 0924-090X, 06/2017, Volume 88, Issue 4, pp. 3017 - 3021
We study two (3\[+\]1)-dimensional generalized equations, namely the Kadomtsev–Petviashvili–Boussinesq equation and the B-type... 
Generalized KP equation | BKP equation | Boussinesq equation | Simplified Hirota’s method | Mathematical analysis | Solitary waves | Boussinesq equations
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20. Full Text Constructing lump solutions to a generalized Kadomtsev–Petviashvili–Boussinesq equation
by Lü, Xing and Chen, Shou-Ting and Ma, Wen-Xiu
Nonlinear Dynamics, ISSN 0924-090X, 10/2016, Volume 86, Issue 1, pp. 523 - 534
Associated with the prime number p = 3, a combined model of generalized bilinear Kadomtsev-Petviashvili and Boussinesq equation (gbKPB for short) in terms of... 
Generalized bilinear operator | Lump solution | Generalized Kadomtsev–Petviashvili–Boussinesq equation | POLYNOMIALS | RATIONAL SOLUTIONS | INTEGRABILITY | WAVES | MECHANICS | Generalized Kadomtsev-Petviashvili-Boussinesq equation | SYMBOLIC COMPUTATION | BILINEAR EQUATIONS | ENGINEERING, MECHANICAL | Resveratrol | Quadratic equations | Boussinesq equations | Parameters | Prime numbers | Searching | Mathematical analysis | Mathematical models | Localization | Density
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