Exact solutions of the coupled Higgs equation and the Maccari system using the modified simplest equation method

New solitary wave solutions of Maccari system

“…In this section, we seek the exact solutions of Maccari system (Maccari, 1996;Rostamy et al, 2011;Jabbari et al, 2011;Zhao, 2008;Zhang, 2007;Wazwaz, 2012;Rostamy and Zabihi, 2012;Abdou et al, 2012;Bekir, 2009;El-Ganaini, 2012;Ye and Zhang, 2011;Manafian and Zamanpour, 2013;Lee and Sakthivel, 2013;Akbari, 2013;Kumar and Chand, 2013;Malik et al, 2012;Li-Na and Qing, 2005;Jun-Ting and Lun-Xun, 2007;Huang et al, 2007;Mirzazadeh, 2015;Ahmed et al, 2013;Hafez et al, 2015;MohyudDin and Shakeel, 2013) by using extended trial equation method.…”

“…Many authors have used to find exact solutions a lot of methods of Maccari system such as exp À ΦðξÞ À Á Àexpansion method, extended F-expansion method, projective Ricatti equation method, first integral method, the tanh-coth method, the sech-csch method, the sec-tan ansatz method, the rational sinh-cosh ansatz method, G 0 =G À Á Àexpansion method, mapping method, lie symmetry approach, He's semi-inverse method, exp-function method, Kudryashov method, the modified simplest equation method, the extended homogeneous balance method, bifurcation theory, extended sine-Gordon equation method, variable separation approach, sine-cosine method and the generalized algebraic method (Maccari, 1996;Rostamy et al, 2011;Jabbari et al, 2011;Zhao, 2008;Zhang, 2007;Wazwaz, 2012;Rostamy and Zabihi, 2012;Abdou et al, 2012;Bekir, 2009;El-Ganaini, 2012;Ye and Zhang, 2011;Manafian and Zamanpour, 2013;Lee and Sakthivel, 2013;Akbari, 2013;Kumar and Chand, 2013;Malik et al, 2012;LiNa and Qing, 2005;Jun-Ting and Lun-Xun, 2007;Huang et al, 2007;Mirzazadeh, 2015;Ahmed et al, 2013;Hafez et al, 2015;Mohyud-Din and Shakeel, 2013).…”

Topological and non-topological soliton solutions of Hamiltonian amplitude equation by He’s semi-inverse method and ansatz approach

“…Then, in Eq. (11), j is the soliton frequency, while x is the wave number of the soliton and h is the phase constant. Finally in Eq.…”

“…This method is introduced by He [1] and it is known He's semiinverse variational principle. In last years, it is used commonly to obtain soliton solutions of NLPDEs and systems by many authors [2][3][4][5][6][7][8][9][10][11]. Biswas et al [5][6][7][8][9] obtained optical solitons and soliton solutions with higher order dispersion by using the He's variational principle.…”

Regularity and Chaos in the Hydrogen Atom Highly Excited with a Strong Magnetic Field

“…Its great importance lies in its implication in different branches of physics: astrophysics [9,12], atomic physics [14][15][16][17], molecular physics [18,19], spectroscopy [20,21], solid state [22], and plasma physics [23]. It leads to interesting quantum features such as soliton propagation [24][25][26][27][28][29][30], entanglement [31,32], antibunching [33], squeezing [34], bistability [35], and chaos [36,37].…”