Kosice, the second largest city of Slovakia, has come up with a bright and brilliant solution to spruce up a nondescript residential district.
Based on the Nth-iterated generalized DT formula, the vector bright soliton solution and vector rogue wave solution have been systematically derived for the coherently coupled nonlinear Schrödinger system [9].
The bright soliton solution (2) exists for (lambda c>0).
Due to the exponential decay of the bright soliton solution [5] when (|x|rightarrowinfty), the conserved quantities (6 - 9) are well defined.
To study the behavior of a single bright soliton solution, we choose the initial condition psi x,0)=Aoperatorname{sech}(beta x exp(ivx) and the homogenous Dirichlet boundary conditions (psi x,0)=0) at (x=x_{L},x_{R}).
The single bright soliton solution of Eq. (1) is given by Biswas [1, 3] as psi x,t)=Aoperatorname{sech}bigl(beta x-ct bigr)exp beta x-ct bigra t)bigr), (2) whexp bigl=Asqrt{2lambda c}quad text{and}quad omega= frac{c(2lambda A^{2}-c)}{2}, (3) A is the amplitude of the soliton, β is the inverse width of the soliton, cx+omega solit bigrlocity, and ω is the wave number.
The brightest solutions come from very simple but innovative ideas.
N, N′-diisopropylbenzamide (0.41 g, 2 mmol) was then introduced and the mixture was stirred for 18 h affording a bright orange solution that was filtered and concentrated by removing some solvent under vacuum.
The mixture turned into a bright blue solution after the addition of 1.5 mL ethanolamine.
