Abundant Exact Solition-Like Solutions to the Generalized Bretherton Equation with Arbitrary Constants

and Applied Analysis 3 V = ±√−α − 5B 2 β + 20CAβ, δ = 4β (−8CAB 2 + B 4 + 16A 2 C 2 ) , (8b) where A, B, and C are arbitrary constants, but C cannot be zero. Case 3. One has a −1 = 0, a 2 = 0, a 1 = 0, a −2 = 2A 2 √ 30β γ , a 0 = 2AC√ 30β γ , B = 0, V = ±√−α − 60CAβ, δ = −16βA 2 C 2 . (8c) Case 4. One has a −1 = 0, a 2 = 0, a 1 = 0, a −2 = 2A 2 √ 30β γ , a 0 = − −15 ± √165 15 CA√ 30β γ , B = 0, V = ε√−α + (−30 ± 2√165)CAβ, δ = −4A 2 C 2 β (13 ± √165) , (8d) where A, B, and C are arbitrary constants, but A cannot be zero. Case 5. One has a −1 = 0, a 2 = 0, a 1 = 0, a −2 = −2A 2 √ 30β γ , a 0 = −2AC√ 30β γ , B = 0, V = ±√−α − 60CAβ, δ = −16BA 2 C 2 . (8e) Case 6. One has a −1 = 0, a 2 = 0, a 1 = 0, a −2 = −2A 2 √ 30β γ , a 0 = (−15 ± √165)CA