It is well-known that for the Sine-Gordon equation, $u_{xt}=\sin u$, if we start with the initial condition resp. initial potential $q(x,0)=\lambda\operatorname{sech}(\lambda x+\mu)$, one can use the inverse scattering transform to get the 1-soliton solution $$ u(x,t)=-4\arctan(e^{\mu+\lambda x+t/\lambda}).\tag{1} $$ (For $\lambda>0$ it is called kink.)
Now I would like to know with which potential we need to start to get the 2-soliton solution (via inverse scattering) $$ u(x,t)=4\arctan\left(\left(\frac{\lambda_1+\lambda_2}{\lambda_1-\lambda_2}\right)\frac{e^{\theta_1}-e^{\theta_2}}{1+e^{\theta_1+\theta_2}}\right),\tag{2} $$ where $\theta_i:=\lambda_i x+t/\lambda_i +\mu_i, i=1,2$.
Something which came into my mind was just something like $$ q(x,0)=\sum_{i=1}^2\lambda_i\operatorname{sech}(\lambda_i x +\mu_i) $$ but this is far from being justified...